How do you do vector cross products?

Question

for example:

Given the vectors
A = 2i - 3j and B = 4j - 5k, calculate A x B

please help me, thanks

Answer 1

Let P = A x B, and
k = i x j, i = j x k, and j = k x i
P = ABsinθ
normal to both A and B
A x B = (2i + 3(-j))(4j + 5(-k))
A x B = 2i x 4j + 2i x 5(-k) + 3(-j) x 4j +3(-j) x 5(-k)
The angle between unit vectors is nπ/2, n = {0,1,2,3}
P = (2)(4)(1)k + (2)(5)(1)(-j) + (3)(4)(0)j +(3)(5)(1)i
P = 15i -10j + 8k
|P| = sqrt(64 + 100 + 225) = 19.732