The cross product of two vectors A and B is a vector perpendicular to the two vectors, the direction determined by the right-hand rule, and its magnitude is || A || * || B || * sin(theta), where theta is the angle between the two.
The formula for the cross product is a little more complicated than the simple formula for the dot product, but it's not bad:A `X B is the determinant of the matrix whose first row is [ i, j, k ], whose second row is [ A_1, A_2, A_3 ], the coefficients of the A vector, and whose third row is [ B_1, B_2, B_3 ], the coefficients of the B vector.
Experience shows that students who have succeeded on Assignments 1-3 typically do not require a q_a_ for this assignment, and may move directly to the Query.
For your convenience here's a listing of the Query questions:
1) 9.4.6 Find v X w when v = 10i - 2j + 4k and w =-i -(1/2)j - 3k. (Where X denotes the cross product)
2) 9.4.10 Find v X w when v = sin(theta)i + cos(theta)j and w = -cos(theta)i + sin(theta)j (theta is any angle).
3) 9.4.12 Find sin(theta) where theta is the angle between v = -i + j and w = -i + j + 2k.
4) 9.4.16 Find a unit vector which is orthogonal to both v = -i + 3j and w = i - j - k
5) 9.4.18 Find a unit vector which is orthogonal to both v = 2i - j and w = 2j - k.
6) 9.4.22 Find the area of the parallelogram determined by the vectors v = 4i + k and w = 4j - k.
7) 9.4.24 Find the area of the triangle with vertices P(2,0,0), Q(1,1,-1), R(3,1,2).
8) 9.4.28 Determine if each of the following products is a vector, scalar, or not defined at all. Explain why. u X (v X w) , u dot (v dot w), (u X v) dot (w X r).
9) 9.4.30 Find the area of the parallelepiped determined by u = i - j, v = i - 2k, and w = 4k
10) 9.4.38 Find a number t such that the vectors -i - j, i - (1/2) j + (1/2)k and -2i -2j - 2tk all lie in the same plane.
11) 9.4.39 u = 2i + 2j, v= i-(1/2)j+ (1/2)k, w = i. Compute (u X v) X w and u X (v X w). What does this say about the associativity of the cross product?