MAT2500-03/04 09S Quiz 1 Print Name (Last, First) _________________________________|__Show all work, including mental steps, in a clearly organized way that speaks for itself. Use proper mathematical notation, identifying expressions by their proper symbols (introducing them if necessary), and use arrows and equal signs when appropriate. Always simplify expressions. BOX final short answers. LABEL parts of problem. Keep answers EXACT (but give decimal approximations for interpretation). Indicate where technology is used and what type (Maple, GC).Given three points 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 : a) Evaluate the lengths of the three difference vectors 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 , 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 and 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 exactly and numerically to 2 decimal place accuracy.
b) Find the angle between 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 and 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 exactly in radians (as an inverse trig expression) and numerically in degrees to 1 decimal place accuracy.
c) Knowing the lengths of three sides of the triangle and the one angle between them from parts a) and b), make a rough sketch of this triangle in its own plane, labeling the 3 vertices and three difference vector sides with arrow heads at their terminal points.d) Find the vector component 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 of 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 along 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 and the vector component 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 perpendicular to 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 both exactly and numerically to 2 decimal place accuracy. [Use the dot product to check that your last result is perpendicular to the direction along which we are projecting.]e) In your sketch of the triangle above, include and label the two projection vectors (arrowheads at their terminal points) and the rectangle associated with the projection/decomposition process you evaluated. solutiona) We introduce the position vectors and the two relevant difference vectorsLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEocmVzdGFydEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GLDYjUSFGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0YzUSdub3JtYWxGJw==Qyg+SSNyMUc2Ii1JJDwsPkdJKF9zeXNsaWJHRiU2JSIiIkYqRiohIiI+SSNyMkdGJS1GJzYlIiIhRioiIiNGKz5JI3IzR0YlLUYnNiVGKkYxRjBGKw==Qyc+SSRyMjFHNiIsJkkjcjJHRiUiIiJJI3IxR0YlISIiRig+SSRyMzFHRiUsJkkjcjNHRiVGKEYpRipGKD5JJHIzMkdGJSwmRi5GKEYnRio=Next we find the corresponding lengths and unit vectorsQy0+SSdyMjFtYWdHNiItSSVzcXJ0RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YlNiMtSTBkZWxheURvdFByb2R1Y3RHNiRGKS9JK21vZHVsZW5hbWVHRiVJLFR5cGVzZXR0aW5nR0YoNiRJJHIyMUdGJUYzIiIiLUkmZXZhbGZHRik2JEkiJUdGJSIiJUY0PkkncjMxbWFnR0YlLUYnNiMtRi02JEkkcjMxR0YlRkBGNEY1RjQ+SSdyMzJtYWdHRiUtRic2Iy1GLTYkSSRyMzJHRiVGR0Y0RjU=QyY+SSdyMjFoYXRHNiIqJkkkcjIxR0YlIiIiLUklc3FydEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYjLUkwZGVsYXlEb3RQcm9kdWN0RzYkRiwvSSttb2R1bGVuYW1lR0YlSSxUeXBlc2V0dGluZ0dGKzYkRidGJyEiIkYoPkkncjMxaGF0R0YlKiZJJHIzMUdGJUYoLUYqNiMtRjA2JEY6RjpGNkYoThen we compute their dot product and arccosine and convert to degreesQyktSTBkZWxheURvdFByb2R1Y3RHNiQlKnByb3RlY3RlZEcvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0c2JEYmSShfc3lzbGliR0YpNiRJJ3IyMWhhdEdGKUkncjMxaGF0R0YpIiIiLUknYXJjY29zR0YpNiNJIiVHRilGMC1JJmV2YWxmR0YmNiMsJComRjRGMEkjUGlHRiYhIiIiJCE9RjAqJi1GNjYkRjQiIiRGMEkoZGVncmVlc0dGKUYwd) Now we evaluate the scalar projection of the first vector along the second, and then multiply the direction of the second by this scalar, then subtract from the first vector to get the orthogonal vector component. Then evaluate the length of the orthogonal vector component.Qy0tSTBkZWxheURvdFByb2R1Y3RHNiQlKnByb3RlY3RlZEcvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0c2JEYmSShfc3lzbGliR0YpNiRJJHIyMUdGKUkncjMxaGF0R0YpIiIiLUkmZXZhbGZHRiY2JEkiJUdGKSIiJUYwPkkncjIxcGFyR0YpLUYkNiRJIyUlR0YpRi9GMD5JKHIyMXBlcnBHRiksJkYuRjBGNCEiIkYwL0YuLCZGN0YwRjxGMEYwLUYkNiRGN0Y8QyUtSSVzcXJ0RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMtSTBkZWxheURvdFByb2R1Y3RHNiRGJi9JK21vZHVsZW5hbWVHRihJLFR5cGVzZXR0aW5nR0YlNiRJKHIyMXBlcnBHRihGMSIiIi1JJmV2YWxmR0YmNiRJIiVHRigiIiU=c),e) Here is the 3d plot exactly of all these points and vectors (they all happen to lie in the plane of the original 3 position vectors, which are coplanar). To rotate this so we are looking at the plane from a right angle, I include a vector perpendicular to the plane so that we can rotate it so we look straight down the vector at the planeQyQtSSV3aXRoRzYiNiNJJnBsb3RzRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YlISIiQyU+SSJORzYiLUkyZGVsYXlDcm9zc1Byb2R1Y3RHNiQlKnByb3RlY3RlZEcvSSttb2R1bGVuYW1lR0YlSSxUeXBlc2V0dGluZ0c2JEYpSShfc3lzbGliR0YlNiRJJHIyMUdGJUkkcjMxR0YlIiIiPkklTmhhdEdGJSomRiRGMi1JJXNxcnRHRi02Iy1JMGRlbGF5RG90UHJvZHVjdEdGKDYkRiRGJCEiIg==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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=TTdSMApJNVJUQUJMRV9TQVZFLzUyMjA4MjUyWColKWFueXRoaW5nRzYiNiJbZ2whIyUhISEiJCIkISIiIiIhIiIiRiY=TTdSMApJNVJUQUJMRV9TQVZFLzUyNDAwMjI4WColKWFueXRoaW5nRzYiNiJbZ2whIyUhISEiJCIkIiIhIiIiISIiRiY=TTdSMApJNVJUQUJMRV9TQVZFLzYzMDgyMzU2WColKWFueXRoaW5nRzYiNiJbZ2whIyUhISEiJCIkIiIiRichIiNGJg==TTdSMApJNVJUQUJMRV9TQVZFLzYzNzc2NTEyWColKWFueXRoaW5nRzYiNiJbZ2whIyUhISEiJCIkLCQqJCIiIyMiIiJGKSMhIiJGKSIiISwkRihGKkYmTTdSMApJNVJUQUJMRV9TQVZFLzUxOTIwMjU2WColKWFueXRoaW5nRzYiNiJbZ2whIyUhISEiJCIkIiIhLCQqJCIiIyMiIiJGKkYrLCRGKSMhIiJGKkYmTTdSMApJNVJUQUJMRV9TQVZFLzUxOTQyNTY0WColKWFueXRoaW5nRzYiNiJbZ2whIyUhISEiJCIkIiIhIyEiIiIiIyMiIiJGKkYmTTdSMApJNVJUQUJMRV9TQVZFLzYzMjQyNTQwWColKWFueXRoaW5nRzYiNiJbZ2whIyUhISEiJCIkISIiIyIiIiIiI0YoRiY=TTdSMApJNVJUQUJMRV9TQVZFLzUyMjA4MjUyWColKWFueXRoaW5nRzYiNiJbZ2whIyUhISEiJCIkISIiIiIhIiIiRiY=TTdSMApJNVJUQUJMRV9TQVZFLzUxMTkzODYwWColKWFueXRoaW5nRzYiNiJbZ2whIyUhISEiJCIkISIiIiIhIiIiRiY=TTdSMApJNVJUQUJMRV9TQVZFLzYyNzIzMjIwWColKWFueXRoaW5nRzYiNiJbZ2whIyUhISEiJCIkISIiRidGJ0YmTTdSMApJNVJUQUJMRV9TQVZFLzYzMDc2OTgwWColKWFueXRoaW5nRzYiNiJbZ2whIyUhISEiJCIkLCQqJCIiJCMiIiIiIiMjISIiRilGJ0YnRiY=