For the unit vectors i, j and k, find i x j , j x k and k x i. What is j x i ?

If A and B are parallel, what is A x B?
If A and B are orthogonal, What is ||A x B|| ?

1 answer

To find the cross product of two vectors, we can use the following properties:

i x j = k
j x k = i
k x i = j
j x i = -k (cross product is anti-commutative)

Therefore, i x j = k, j x k = i, k x i = j, and j x i = -k.

If A and B are parallel, their cross product is a zero vector: A x B = 0.

If A and B are orthogonal (perpendicular), the magnitude of their cross product is equal to the product of their magnitudes: ||A x B|| = ||A|| * ||B||.