Scratchpad calculations for Stewart 8e Example 12.2.7
after solving by hand [using Maple Document Mode] 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 is an example of how one can use Maple document mode to evaluate formulas numerically, including vectors (use the < and > characters as delimiters). Maple trig functions assume radian angles, so the degree angles must be converted to radians.
First we evaluate the magnitude of the first tension vector, then rightclicking on its numerical value allows us to assign it to the symbol T1, then we obtain T2 and repeat, then easily evaluate the vector components of each vector.LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRidGKy1JJ21zcGFjZUdGJDYmLyUnaGVpZ2h0R1EmMC4wZXhGJy8lJndpZHRoR1EmMC4wZW1GJy8lJmRlcHRoR0Y0LyUqbGluZWJyZWFrR1EobmV3bGluZUYnLUkmbWZyYWNHRiQ2KC1JI21uR0YkNiRRJDEwMEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1GIzYmRistSShtZmVuY2VkR0YkNiQtRiM2KkYrLUYjNiYtRiw2JVEkc2luRicvJSdpdGFsaWNHUSV0cnVlRicvRkVRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEwJkFwcGx5RnVuY3Rpb247RidGRC8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGaG4vJSlzdHJldGNoeUdGaG4vJSpzeW1tZXRyaWNHRmhuLyUobGFyZ2VvcEdGaG4vJS5tb3ZhYmxlbGltaXRzR0Zobi8lJ2FjY2VudEdGaG4vJSdsc3BhY2VHRjcvJSdyc3BhY2VHRjctRko2JC1GIzYmRistRj42KC1GIzYmLUZBNiRRIzUwRidGRC1GWTYtUScmc2RvdDtGJ0ZERmZuRmluRltvRl1vRl9vRmFvRmNvL0Zmb1EsMC4yMjIyMjIyZW1GJy9GaG9GaHAtRiw2JVEnJiM5NjA7RidGU0ZWRkQtRkE2JFElMTgwLkYnRkQvJS5saW5ldGhpY2tuZXNzR1EiMUYnLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRmVxLyUpYmV2ZWxsZWRHRmhuRitGREZERkQtRlk2LVEnJnBsdXM7RidGREZmbkZpbkZbb0Zdb0Zfb0Zhb0Zjb0ZncEZpcC1GIzYmLUYsNiVRJGNvc0YnRlNGVkZYLUZKNiQtRiM2JkYrLUY+NigtRiM2JkZhcC1GWTYtRmZwRkRGZm5GaW5GW29GXW9GX29GYW9GY29GZW9GZ29GanBGREZdcUZgcUZjcUZmcUZocUYrRkRGREZERmpyLUYjNiYtRiw2JVEkdGFuRidGU0ZWRlgtRko2JC1GIzYmRistRj42KC1GIzYmLUZBNiRRIzMyRidGREZqckZqcEZERl1xRmBxRmNxRmZxRmhxRitGREZERkRGK0ZERkRGK0ZERmBxRmNxRmZxRmhxRkQ=LUkmbW92ZXJHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JS1JI21vR0YkNi9RJyZyYXJyO0YnLyUrZXhlY3V0YWJsZUdRJXRydWVGJy8lMGZvbnRfc3R5bGVfbmFtZUdRKDJEfk1hdGhGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjovJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGOi8lKGxhcmdlb3BHRjovJS5tb3ZhYmxlbGltaXRzR0Y6LyUnYWNjZW50R0Y6LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGSS1JJm10ZXh0R0YkNiZRMWFzc2lnbn50b35hfm5hbWVGJ0YvRjJGNUZFLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYxLUkjbWlHRiQ2KVEjVDFGJy8lJ2ZhbWlseUdRMFRpbWVzfk5ld35Sb21hbkYnLyUlYm9sZEdRJmZhbHNlRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EoWzAsMCwwXUYnLyUrZXhlY3V0YWJsZUdGNC8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYxUSJ+RidGL0YyRjhGOy9GPlEnbm9ybWFsRicvJSZmZW5jZUdGNC8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZWLUZBNjFRKCYjODc4ODtGJ0YvRjJGOEY7RkRGRkZIRkpGTEZORlBGUkZURldGQC1JKG1hY3Rpb25HRiQ2JS1JKm12ZXJiYXRpbUdGJDYjUS0kIiswTiNRYykhIilGJy8lK2FjdGlvbnR5cGVHUThtYXBsZXNvZnQuY29tOmxhYmVsKEwyKUYnLyUldmlld0dRJmxhYmVsRictRkE2MVEiOkYnRi9GMkY4RjtGREZGRkhGSkZMRk5GUEZSL0ZVUSwwLjI3Nzc3NzhlbUYnL0ZYRmdvRkAtRkE2MVEiJ0YnRi9GMkY4RjtGREZGRkhGSkZMRk5GUEZSL0ZVUSwwLjExMTExMTFlbUYnRldGK0Zpb0YvRjJGOEY7RkQ=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEiJUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RJyZzZG90O0YnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZMLUkmbWZyYWNHRiQ2KC1GIzYmLUYsNiNRIUYnLUYjNiYtRiw2JVEkY29zRidGL0YyLUY2Ni1RMCZBcHBseUZ1bmN0aW9uO0YnRjlGO0Y+RkBGQkZERkZGSEZKRk0tSShtZmVuY2VkR0YkNiQtRiM2JkZULUZQNigtRiM2Ji1JI21uR0YkNiRRIzUwRidGOUY1LUYsNiVRJyYjOTYwO0YnRi9GMkY5LUZjbzYkUSUxODAuRidGOS8lLmxpbmV0aGlja25lc3NHUSIxRicvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGYXAvJSliZXZlbGxlZEdGPUZURjlGOUY5RlRGOS1GIzYmRlQtRiM2JkZZRmZuLUZqbjYkLUYjNiZGVC1GUDYoLUYjNiYtRmNvNiRRIzMyRidGOUY1RmZvRjlGaW9GXHBGX3BGYnBGZHBGVEY5RjlGOUZURjlGXHBGX3BGYnBGZHBGVEY5LUkmbW92ZXJHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JS1JI21vR0YkNi9RJyZyYXJyO0YnLyUrZXhlY3V0YWJsZUdRJXRydWVGJy8lMGZvbnRfc3R5bGVfbmFtZUdRKDJEfk1hdGhGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjovJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGOi8lKGxhcmdlb3BHRjovJS5tb3ZhYmxlbGltaXRzR0Y6LyUnYWNjZW50R0Y6LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGSS1JJm10ZXh0R0YkNiZRMWFzc2lnbn50b35hfm5hbWVGJ0YvRjJGNUZFLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYxLUkjbWlHRiQ2KVEjVDJGJy8lJ2ZhbWlseUdRMFRpbWVzfk5ld35Sb21hbkYnLyUlYm9sZEdRJmZhbHNlRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EoWzAsMCwwXUYnLyUrZXhlY3V0YWJsZUdGNC8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYxUSJ+RidGL0YyRjhGOy9GPlEnbm9ybWFsRicvJSZmZW5jZUdGNC8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZWLUZBNjFRKCYjODc4ODtGJ0YvRjJGOEY7RkRGRkZIRkpGTEZORlBGUkZURldGQC1JKG1hY3Rpb25HRiQ2JS1JKm12ZXJiYXRpbUdGJDYjUS0kIis6bC8iXCchIilGJy8lK2FjdGlvbnR5cGVHUTltYXBsZXNvZnQuY29tOmxhYmVsKEwxMilGJy8lJXZpZXdHUSZsYWJlbEYnLUZBNjFRIjpGJ0YvRjJGOEY7RkRGRkZIRkpGTEZORlBGUi9GVVEsMC4yNzc3Nzc4ZW1GJy9GWEZnb0ZALUZBNjFRIidGJ0YvRjJGOEY7RkRGRkZIRkpGTEZORlBGUi9GVVEsMC4xMTExMTExZW1GJ0ZXRitGaW9GL0YyRjhGO0ZEJSFHLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkobWZlbmNlZEdGJDYmLUYjNi0tSSNtb0dGJDYtUSomdW1pbnVzMDtGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjkvJSlzdHJldGNoeUdGOS8lKnN5bW1ldHJpY0dGOS8lKGxhcmdlb3BHRjkvJS5tb3ZhYmxlbGltaXRzR0Y5LyUnYWNjZW50R0Y5LyUnbHNwYWNlR1EsMC4yMjIyMjIyZW1GJy8lJ3JzcGFjZUdGSC1JI21pR0YkNiVRI1QxRicvJSdpdGFsaWNHUSV0cnVlRicvRjVRJ2l0YWxpY0YnLUYxNi1RIn5GJ0Y0RjdGOkY8Rj5GQEZCRkQvRkdRJjAuMGVtRicvRkpGWC1GTDYlUSRjb3NGJy9GUEY5RjQtRiw2JC1GIzYmLUZMNiNRIUYnLUkmbWZyYWNHRiQ2KC1GIzYmLUkjbW5HRiQ2JFEjNTBGJ0Y0LUYxNi1RJyZzZG90O0YnRjRGNy9GO0ZRRjxGPkZARkJGREZXL0ZKUSwwLjMzMzMzMzNlbUYnLUZMNiVRJyYjOTYwO0YnRk9GUkY0LUZlbzYkUSUxODAuRidGNC8lLmxpbmV0aGlja25lc3NHUSIxRicvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGaXAvJSliZXZlbGxlZEdGOUZcb0Y0RjQtRjE2LVEiLEYnRjRGN0ZbcEY8Rj5GQEZCRkRGV0ZccEZLRlQtRkw2JVEkc2luRidGZ25GNC1GLDYkLUYjNiRGX29GNEY0RjRGNC8lJW9wZW5HUScmbGFuZztGJy8lJmNsb3NlR1EnJnJhbmc7RidGNA==LUkmbW92ZXJHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JS1JI21vR0YkNi9RJyZyYXJyO0YnLyUrZXhlY3V0YWJsZUdRJXRydWVGJy8lMGZvbnRfc3R5bGVfbmFtZUdRKDJEfk1hdGhGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjovJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGOi8lKGxhcmdlb3BHRjovJS5tb3ZhYmxlbGltaXRzR0Y6LyUnYWNjZW50R0Y6LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGSS1JJm10ZXh0R0YkNiZRLGF0fjV+ZGlnaXRzRidGL0YyRjVGRQ==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 that in Document Mode the results of the context sensitive menu choices are indicated only by an arrow (or an annotated arrow), while in Worksheet Mode the Maple command is inserted giving a clue as to how each expression relates to the next one. This is why Worksheet mode is usually a better environment for us to work in.
[The percent sign % stands for the previous result and is a useful shorthand.]USEFUL OBSERVATIONS.1) By solving the problem symbolically in terms of the two angles of 50 and 32 degrees before evaluating trig functions to numbers, we have in effect solved all possible two wire hanging mass tension problems at once (just replace the 50 and 32 by the pair of angles in the problem).2) By not using numerical values in preliminary formulas, we obtained exact final formulas that we can then evaluate to any accuracy we desire, without danger of error propagation from using too few digits on intermediate evaluations.3) We need to think about significant digits in the final answer. Keeping more than one decimal place is unwarranted, so these values should be rounded at least to one decimal place, if not integers.worksheet approach to same problem (easier to edit for new parameter values)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a useful plot (plus Explore slider bonus)Their is no need to understand the plot commands. Visualization is very helpful though.LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEld2l0aEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYlLUYsNiVRJnBsb3RzRidGL0YyLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvRjNRJ25vcm1hbEYnRkAtSSNtb0dGJDYtUSI6RidGQC8lJmZlbmNlR0Y/LyUqc2VwYXJhdG9yR0Y/LyUpc3RyZXRjaHlHRj8vJSpzeW1tZXRyaWNHRj8vJShsYXJnZW9wR0Y/LyUubW92YWJsZWxpbWl0c0dGPy8lJ2FjY2VudEdGPy8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRlZGPUZAWe introduce the two tension vectors and plot them together with their vector sum parallelogram, and projections down to the horizontal axis.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Now lets convert the fixed angles in the plot to sliders.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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=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
SSZhbHBoYUc2Ig==#
# The following code is autogenerated by the Explore command. Do not edit.
#
Explore:-Runtime:-Update( plots:-display(plots:-arrow(Vector(2, [-100/(sin(.1745329252e-1*alpha)+cos(.1745329252e-1*alpha)*tan(.1745329252e-1*beta))*cos(.1745329252e-1*alpha),100/(sin(.1745329252e-1*alpha)+cos(.1745329252e-1*alpha)*tan(.1745329252e-1*beta))*sin(.1745329252e-1*alpha)]),shape = plots:-arrow,color = red,thickness = 2,head_width = [5]),plots:-arrow(Vector(2, [100/(sin(.1745329252e-1*alpha)+cos(.1745329252e-1*alpha)*tan(.1745329252e-1*beta))*cos(.1745329252e-1*alpha),100/(sin(.1745329252e-1*alpha)+cos(.1745329252e-1*alpha)*tan(.1745329252e-1*beta))*cos(.1745329252e-1*alpha)/cos(.1745329252e-1*beta)*sin(.1745329252e-1*beta)]),shape = plots:-arrow,color = red,thickness = 2,head_width = [5]),plots:-arrow((Vector(2, [-100/(sin(.1745329252e-1*alpha)+cos(.1745329252e-1*alpha)*tan(.1745329252e-1*beta))*cos(.1745329252e-1*alpha),100/(sin(.1745329252e-1*alpha)+cos(.1745329252e-1*alpha)*tan(.1745329252e-1*beta))*sin(.1745329252e-1*alpha)]))+(Vector(2, [100/(sin(.1745329252e-1*alpha)+cos(.1745329252e-1*alpha)*tan(.1745329252e-1*beta))*cos(.1745329252e-1*alpha),100/(sin(.1745329252e-1*alpha)+cos(.1745329252e-1*alpha)*tan(.1745329252e-1*beta))*cos(.1745329252e-1*alpha)/cos(.1745329252e-1*beta)*sin(.1745329252e-1*beta)])),shape = plots:-arrow,color = red,thickness = 2,head_width = [5]),plots:-arrow(-(Vector(2, [-100/(sin(.1745329252e-1*alpha)+cos(.1745329252e-1*alpha)*tan(.1745329252e-1*beta))*cos(.1745329252e-1*alpha),100/(sin(.1745329252e-1*alpha)+cos(.1745329252e-1*alpha)*tan(.1745329252e-1*beta))*sin(.1745329252e-1*alpha)]))-(Vector(2, [100/(sin(.1745329252e-1*alpha)+cos(.1745329252e-1*alpha)*tan(.1745329252e-1*beta))*cos(.1745329252e-1*alpha),100/(sin(.1745329252e-1*alpha)+cos(.1745329252e-1*alpha)*tan(.1745329252e-1*beta))*cos(.1745329252e-1*alpha)/cos(.1745329252e-1*beta)*sin(.1745329252e-1*beta)])),shape = plots:-arrow,color = blue,thickness = 2,head_width = [10]),PLOT(CURVES([[-100/(sin(.1745329252e-1*alpha)+cos(.1745329252e-1*alpha)*tan(.1745329252e-1*beta))*cos(.1745329252e-1*alpha), 0], [-100/(sin(.1745329252e-1*alpha)+cos(.1745329252e-1*alpha)*tan(.1745329252e-1*beta))*cos(.1745329252e-1*alpha), 100/(sin(.1745329252e-1*alpha)+cos(.1745329252e-1*alpha)*tan(.1745329252e-1*beta))*sin(.1745329252e-1*alpha)], [0, 100/(sin(.1745329252e-1*alpha)+cos(.1745329252e-1*alpha)*tan(.1745329252e-1*beta))*sin(.1745329252e-1*alpha)+100/(sin(.1745329252e-1*alpha)+cos(.1745329252e-1*alpha)*tan(.1745329252e-1*beta))*cos(.1745329252e-1*alpha)/cos(.1745329252e-1*beta)*sin(.1745329252e-1*beta)], [100/(sin(.1745329252e-1*alpha)+cos(.1745329252e-1*alpha)*tan(.1745329252e-1*beta))*cos(.1745329252e-1*alpha), 100/(sin(.1745329252e-1*alpha)+cos(.1745329252e-1*alpha)*tan(.1745329252e-1*beta))*cos(.1745329252e-1*alpha)/cos(.1745329252e-1*beta)*sin(.1745329252e-1*beta)], [100/(sin(.1745329252e-1*alpha)+cos(.1745329252e-1*alpha)*tan(.1745329252e-1*beta))*cos(.1745329252e-1*alpha), 0]]),COLOUR(RGB,.75294118,.75294118,.75294118),THICKNESS(2),AXESLABELS("",""),VIEW(DEFAULT,DEFAULT)),gridlines = true,scaling = constrained), ':-Plot0', [':-alpha', ':-beta'], ':-sliders'=["Slideralpha", "Sliderbeta"], ':-labels'=["Labelalpha", "Labelbeta"],':-isplot'=true, ':-handlers'=[alpha=handlertab[alpha],beta=handlertab[beta]]);
#
# End of autogenerated code.
#
SSViZXRhRzYi#
# The following code is autogenerated by the Explore command. Do not edit.
#
Explore:-Runtime:-Update( plots:-display(plots:-arrow(Vector(2, [-100/(sin(.1745329252e-1*alpha)+cos(.1745329252e-1*alpha)*tan(.1745329252e-1*beta))*cos(.1745329252e-1*alpha),100/(sin(.1745329252e-1*alpha)+cos(.1745329252e-1*alpha)*tan(.1745329252e-1*beta))*sin(.1745329252e-1*alpha)]),shape = plots:-arrow,color = red,thickness = 2,head_width = [5]),plots:-arrow(Vector(2, [100/(sin(.1745329252e-1*alpha)+cos(.1745329252e-1*alpha)*tan(.1745329252e-1*beta))*cos(.1745329252e-1*alpha),100/(sin(.1745329252e-1*alpha)+cos(.1745329252e-1*alpha)*tan(.1745329252e-1*beta))*cos(.1745329252e-1*alpha)/cos(.1745329252e-1*beta)*sin(.1745329252e-1*beta)]),shape = plots:-arrow,color = red,thickness = 2,head_width = [5]),plots:-arrow((Vector(2, [-100/(sin(.1745329252e-1*alpha)+cos(.1745329252e-1*alpha)*tan(.1745329252e-1*beta))*cos(.1745329252e-1*alpha),100/(sin(.1745329252e-1*alpha)+cos(.1745329252e-1*alpha)*tan(.1745329252e-1*beta))*sin(.1745329252e-1*alpha)]))+(Vector(2, [100/(sin(.1745329252e-1*alpha)+cos(.1745329252e-1*alpha)*tan(.1745329252e-1*beta))*cos(.1745329252e-1*alpha),100/(sin(.1745329252e-1*alpha)+cos(.1745329252e-1*alpha)*tan(.1745329252e-1*beta))*cos(.1745329252e-1*alpha)/cos(.1745329252e-1*beta)*sin(.1745329252e-1*beta)])),shape = plots:-arrow,color = red,thickness = 2,head_width = [5]),plots:-arrow(-(Vector(2, [-100/(sin(.1745329252e-1*alpha)+cos(.1745329252e-1*alpha)*tan(.1745329252e-1*beta))*cos(.1745329252e-1*alpha),100/(sin(.1745329252e-1*alpha)+cos(.1745329252e-1*alpha)*tan(.1745329252e-1*beta))*sin(.1745329252e-1*alpha)]))-(Vector(2, [100/(sin(.1745329252e-1*alpha)+cos(.1745329252e-1*alpha)*tan(.1745329252e-1*beta))*cos(.1745329252e-1*alpha),100/(sin(.1745329252e-1*alpha)+cos(.1745329252e-1*alpha)*tan(.1745329252e-1*beta))*cos(.1745329252e-1*alpha)/cos(.1745329252e-1*beta)*sin(.1745329252e-1*beta)])),shape = plots:-arrow,color = blue,thickness = 2,head_width = [10]),PLOT(CURVES([[-100/(sin(.1745329252e-1*alpha)+cos(.1745329252e-1*alpha)*tan(.1745329252e-1*beta))*cos(.1745329252e-1*alpha), 0], [-100/(sin(.1745329252e-1*alpha)+cos(.1745329252e-1*alpha)*tan(.1745329252e-1*beta))*cos(.1745329252e-1*alpha), 100/(sin(.1745329252e-1*alpha)+cos(.1745329252e-1*alpha)*tan(.1745329252e-1*beta))*sin(.1745329252e-1*alpha)], [0, 100/(sin(.1745329252e-1*alpha)+cos(.1745329252e-1*alpha)*tan(.1745329252e-1*beta))*sin(.1745329252e-1*alpha)+100/(sin(.1745329252e-1*alpha)+cos(.1745329252e-1*alpha)*tan(.1745329252e-1*beta))*cos(.1745329252e-1*alpha)/cos(.1745329252e-1*beta)*sin(.1745329252e-1*beta)], [100/(sin(.1745329252e-1*alpha)+cos(.1745329252e-1*alpha)*tan(.1745329252e-1*beta))*cos(.1745329252e-1*alpha), 100/(sin(.1745329252e-1*alpha)+cos(.1745329252e-1*alpha)*tan(.1745329252e-1*beta))*cos(.1745329252e-1*alpha)/cos(.1745329252e-1*beta)*sin(.1745329252e-1*beta)], [100/(sin(.1745329252e-1*alpha)+cos(.1745329252e-1*alpha)*tan(.1745329252e-1*beta))*cos(.1745329252e-1*alpha), 0]]),COLOUR(RGB,.75294118,.75294118,.75294118),THICKNESS(2),AXESLABELS("",""),VIEW(DEFAULT,DEFAULT)),gridlines = true,scaling = constrained), ':-Plot0', [':-alpha', ':-beta'], ':-sliders'=["Slideralpha", "Sliderbeta"], ':-labels'=["Labelalpha", "Labelbeta"],':-isplot'=true, ':-handlers'=[alpha=handlertab[alpha],beta=handlertab[beta]]);
#
# End of autogenerated code.
#
We can also explore the numerical values of the vector components, but the Explore command insists on telling us what these expressions are whose numerical values we want to see.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
SSZhbHBoYUc2Ig==#
# The following code is autogenerated by the Explore command. Do not edit.
#
Explore:-Runtime:-Update( map(evalf,[Vector(2, [-100/(sin(.1745329252e-1*alpha)+cos(.1745329252e-1*alpha)*tan(.1745329252e-1*beta))*cos(.1745329252e-1*alpha),100/(sin(.1745329252e-1*alpha)+cos(.1745329252e-1*alpha)*tan(.1745329252e-1*beta))*sin(.1745329252e-1*alpha)]), Vector(2, [100/(sin(.1745329252e-1*alpha)+cos(.1745329252e-1*alpha)*tan(.1745329252e-1*beta))*cos(.1745329252e-1*alpha),100/(sin(.1745329252e-1*alpha)+cos(.1745329252e-1*alpha)*tan(.1745329252e-1*beta))*cos(.1745329252e-1*alpha)/cos(.1745329252e-1*beta)*sin(.1745329252e-1*beta)])]), ':-Math', [':-alpha', ':-beta'], ':-sliders'=["Slideralpha1", "Sliderbeta1"], ':-labels'=["Labelalpha1", "Labelbeta1"], ':-echoexpression'=true, ':-handlers'=[alpha=handlertab[alpha],beta=handlertab[beta]]);
#
# End of autogenerated code.
#
SSViZXRhRzYi#
# The following code is autogenerated by the Explore command. Do not edit.
#
Explore:-Runtime:-Update( map(evalf,[Vector(2, [-100/(sin(.1745329252e-1*alpha)+cos(.1745329252e-1*alpha)*tan(.1745329252e-1*beta))*cos(.1745329252e-1*alpha),100/(sin(.1745329252e-1*alpha)+cos(.1745329252e-1*alpha)*tan(.1745329252e-1*beta))*sin(.1745329252e-1*alpha)]), Vector(2, [100/(sin(.1745329252e-1*alpha)+cos(.1745329252e-1*alpha)*tan(.1745329252e-1*beta))*cos(.1745329252e-1*alpha),100/(sin(.1745329252e-1*alpha)+cos(.1745329252e-1*alpha)*tan(.1745329252e-1*beta))*cos(.1745329252e-1*alpha)/cos(.1745329252e-1*beta)*sin(.1745329252e-1*beta)])]), ':-Math', [':-alpha', ':-beta'], ':-sliders'=["Slideralpha1", "Sliderbeta1"], ':-labels'=["Labelalpha1", "Labelbeta1"], ':-echoexpression'=true, ':-handlers'=[alpha=handlertab[alpha],beta=handlertab[beta]]);
#
# End of autogenerated code.
#