219. The diagram at right shows a rectangular solid, two of whose vertices are A = (0, 0, 0) and G=(4, 6,3). centi → (a) Find vector projections of AG onto AB, AD, and AE. (b) Find the point on segment AC that is closest to the midpoint of segment GH. F

Q: Show that the points A = (1, 2), B = (1,0), and C = collinear and express P = (-7,0) in barycentric…

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Q: Let P(3,-1,4) and Q(10, 13,9) u = (2,5, -1) and v= (7,-1,2) l be the line through P along direction…

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Q: The parametric vector v=(6-t)i+(9t+8)j represents a straight line. Find the equation of this line

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Q: Parametrize the line segment joining the points P(1, 2, 0) and Q(1, 3, -1).

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Q: If a line is parallel to the vector 4i + 1j + 4k and passes through the point P = (3, 7,9), then the…

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Q: Find parametric equations for the line through the point P(-5,6,7) and perpendicular to the vectors…

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Q: Find a parametric form for the line through the point (0, –7, -9) and parallel to the vector 6i – 7j…

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Q: Show that the points whose position vectors 2i+ 3j – 5k , 3i +j – 2k and 6ỉ – 5j + 7k are collinear?

A: Let the given vectors are  A=2i+3i-5k,B=3i+j-2k,C=6i-5j+7k. Find AB as follows: BA=2-3i+3-1i+-5--2k…

Q: b) The graph below shows dashed vector u and solid vector n. Draw projπ(n).

A: To draw the projection of vector n onto vector u (denoted as proju​(n), follow these steps: Identify…

Q: Let u = 2i - 5j, v = -3i + 7j, and w = -i - 6j.Find specified vector or scalar 3v - 4w.

A: Given  u = 2i - 5j, v = -3i + 7j, and w = -i - 6j. We need to find the specified vector or scalar…