Find the indicated vector.
1) Let u = -8, -2 , v = -3, -6 . Find 4
5u + 3
5v.
A) – 26
5 , – 41
5 B) – 41
5 , – 26
5 C) – 38
5 , – 6 D) – 44
5 , – 24
5
Express the vector in the form ai + bj.
2) P1P2 if P1 is the point (3, -2) and P2 is the point (5, -5)
A) v = -2i – 3j B) v = -2i +3j C) v =-i +3j D) v =2i -3j
Solve the problem.
3) A force of magnitude 11 pounds pulling on a suitcase makes an angle of 30° with the ground. Express the
force in terms of its i and j components.
A) 9.526i + 5.500 j B) 5.500i +9.526j C) 0.8660i ++0.5000j D) 1.697i -10.87j
Express the vector in the form ai + bj + ck.
4) AB if A is the point (-6, -4, 5) and B is the point (-1, -11, 8)
A) v = 5i – 7j – 3k B) v = 5i +7j -3k C) v =5i +7j +3k D) v =5i -7j +3k
Find an equation for the sphere with the given center and radius.
5) Center (-2, 10, 0), radius = 9
A) x2 + y2 + z2 + 4x – 20y = -23 B) x2 + y2 + z2 – 4x + 20y = -23
C) x2 + y2 + z2 + 4x + 20y = -23 D) x2 + y2 + z2 – 4x – 20y = -23
Find v · u.
6) v = -5i + 9j and u = 3i + 8j
A) -87 B) -15i +72j C) -2i +17j D) 57
Find the angle between u and v in radians.
7) u = 9i – 7j – 6k, v = 2i + 9j – 10k
A) 0.09 B) 1.49 C) 1.57 D) 1.53
Find projv u.
8) v = 3i – j + 3k, u = 11i + 2j + 10k
A) 195
19 i – 65
19j + 195
19 k B) 671
15 i + 122
15 j + 122
3 k
C) 671
225i + 122
225j + 122
45 k D) 183
19 i – 61
19j + 183
19 k
Solve the problem.
9) How much work does it take to slide a box 38 meters along the ground by pulling it with a 200 N force at an angle of 13° from the horizontal?
A) 194.9 joules B) 6897 joules C) 7405 joules D) 7600 joules
Find the magnitude of u × v and the unit vector parrallel to u ×v in the direction of u × v.
10) u = 2i + 2j – k, v = -i + k
A) 3; 2
3i + 1
3j – 2
3k B) 9; 2
9i – 1
9j + 2
9k C) 9; 2
9i + 1
9j – 2
9k D) 3; 2
3i – 1
3j + 2
3k
