Math 152 Week in Review Sections 11.2, 11.3 Fall '09

These problems are from Stewart's textbook.

11.2

1. Find the angle between the vectors.

a) a = <6, 0, 2 > b = < 5, 3, -2 >

b) a = i + j b = 2i - 3k

2. Determine whether the vectors are parallel, orthogonal, or neither.

a) a = < -1, 5, 2 > b = < 4, 2, -3 >

b) a = 2i +6j - 4k b = -3i - 9j + 6k

3. Two direction angles of a vector are . Find the third angle.

4. Find the scalar and vector projections of b onto a.

a) a = < 3, -1 > b = < 2, 3 > b) a = 2i - 3j + k b = i + 6j - 2k

5. Find the work done by a 20 lb force acting in the direction N50W in moving an object 4 ft due west.

11.3

6. Find two unit vectors orthogonal to both i + j and i - j + k.

7. Find the area of the parallelogram with vertices P(0,0,0), Q(5,0,0), R(2,6,6) and S(7,6,6).

8. Find the volume of the parallelepiped determined by the vectors

a = 2i + 3j - 2k , b = i - j , and c = 2i + 3k.

9. Find the volume of the parallelepiped with adjacent edges PQ, PR, and PS.

P(0,1,2), Q(2,4,5), R(-1,0,1), and S(6, -1, 4).

10. Use a scalar triple product to determine whether the points P(1,0,1), Q(2,4,6),

R(3, -1, 2), and S(6,2,8) lie in the same plane.

11. Let P be a point not on the plane that passes through the points Q, R, and S. Show that the distance d from P to the plane is where a = QR, b = QS and c = QP.