Describe the graph of the equation. r= (3 – 2) i + 61 j O tis a line in 2-space through the point (3, 2) and parallel to the vector v = 6j. O tis a line in 2-space through the point (-2, 6) and parallel to the vector v = 3i O tis a plane in 2-space through the point (3, 0) and parallel to the vector v = -2i+ 6j. O Itis aline in 2-space through the point (3, 0) and parallel to the vector v = -2i+ 6j. O tis a plane in 2-space through the point (-2, 6) and parallel to the vector v = 31

(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)

Find an equation the plane that passes through the points A(4,0, –5), B(8,-3,-6), and C (1, 2, -1). Write your final answer in standard form.

Find the equation of the plane parallel to the line r = 2i + t(-4i + 8j + 8k) and containing the points (7, 10, 7) and (6, 8, 9). (Express numbers in exact form. Use symbolic notation and fractions where needed.)