Prove the property of the cross product?

Question

u x v = 0 if and only if u and v are scalar multiples of each other.

steps please

Answer 1

The cross product can be written as "u x v", read as "u cross v", or you can write it another way:

|u| * |v| * sin(theta)

read as "the magnitude of u, times the magnitude of v, times the sine of the angle between vectors u and v".

Now, if two vectors are scalar multiples of each other, their direction is the same, but their lengths may be different.

Pointing in the same direction means there is no angle between them. In this case, theta would be zero. The sine of zero is zero, so the cross product is zero.