1. (1 point) Use the algebraic definition to find xif v= -21-J+k and w=-27+27-2k. 2. (1 point) Suppose -w=4 and ||xw|| = 2, and the angle between V and wis 8.

Find (a) tane= (b) 8= 3. (1 point) Ifvxw=47+]+2k, and -w=4, and is the angle between Vand w, then (a) tan (b) 8 = 4. (1 point) Find a unit vector with positive first coordinate that is orthogonal to the plane through the points P = (-2, -5, -5), Q=(3, 0, 0), and R=(3, 0, 2). 5. (1 point) Find the area of the parallelogram with vertices (4,2), (5, 4), (6, 7), and (7,9). Answer: 6. (1 point) If a=i+6j+k and b=i+9j+k, find a unit vector with positive first coordinate orthogonal to both a and b. 7. (1 point) Find the area of the parallelogram with vertices: P(0,0,0), Q(-2,-3,1), R(-2,-1,3), S(-4,-4,4). Generated by Well Work, http://webwork.maa.org, Mathematical Association of America 8. (1 point) Use the geometric definition of the cross product and the properties of the cross product to make the following calcula- tions. (a) ((7+J) × 1) × ]=- (b) (j+k) × (jxk) =. (c) 37 x (1+]) =. (d) (k+7) × (k − 7) =. 9. (1 point) Calculate the cross product assuming that uxw = (-7, 1, 3) (3u-4w) xw= 10. (1 point) The plane that passes through the point (0,-3,5) and is per- pendicular to both z-(3x+y) = 12 and 4x + 3y + 5z = 0 has as its implicit equation. 11. (1 point) Find the area of the parallelogram defined by the vectors Area = 12. (1 point) دا بیا بیا بیا Find the angle between the diagonal of a cube of side length 9 and the diagonal of one of its faces. The angle should be measured in radians.