03* Which of the following is the direction vector from the point A(4, -3, 2, 1) point B(-7,2, -4, 3)? O(-3,-1,-2,4) O(-11,5,-6,2)

(part 1 of 4) Suppose you start at the origin in 3-space, move along the x-axis a distance of 2 units in the positive direction, and then move down- ward a distance of 3 units. What are the coordinates of your position? 1. (2,0, -3) 2. (2, -3,0) 3. (2,0,3) 4. (0, 2, -3) 5. (0, -3,2) (part 2 of 4) Which one of the points P(6, 9, -3), Q(8, -2, -8), R(-5, 8, 1) in 3-space is closest to the xz-plane? 1. R(-5, 8, 1) 2. P(6, 9, -3) 3. Q(8, -2, -8) (part 3 of 4) A rectangular box is constructed in 3-space with one corner at the origin and other ver- tices at (1,0,0), (0,3,0), (0,0,2). Find the length of the diagonal of the box. 1. length 14 2. length 3. length 4. length 5. length 6. length = = = = √22 √14 √19 19 22 (part 4 of 4) What are the coordinates of the projection of the point Q(-4, 5, 3) onto the zx-plane? 1. (-4, 0, 3) 2. (-4, -5, 3) (4, 5, 3) 3. 4. (-4, 5, 0) 5. (-4, 5, -3) 6. (0,5, 3)

The figure below shows two named points A and B in R?. 6 4 A -1 -2 -3 -4 B -5 -6 -6 -5 -4 -3 -2 -1 5 6 1 3 4 > Part 1 Part 2 a. Write the vector BA as a sum of two vectors, one parallel to (1,0) and the other parallel to (0, -2). ВА- + b. Write the vector BA as a sum of two vectors, one parallel to (1, 1) and the other parallel to (-1, 1). BA = +

Find a plane through the points (-2,2,-7), (4,1,8), (7,-1,5)