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|| ?
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||.
To find the cross product of two vectors, you can use the right-hand rule. The cross product of two vectors A and B is denoted as A x B.
1. i x j:
The cross product of i and j is k.
So, i x j = k.
2. j x k:
The cross product of j and k is i.
So, j x k = i.
3. k x i:
The cross product of k and i is j.
So, k x i = j.
4. j x i:
Using the right-hand rule, the cross product of j and i is equal to the negative of i x j.
So, j x i = - (i x j) = -k.
If A and B are parallel vectors, their cross product will be zero.
So, A x B = 0.
If A and B are orthogonal vectors, the magnitude of their cross product is equal to the product of their magnitudes.
So, ||A x B|| = ||A|| * ||B||.