The Vector product (cross product) is a new way to multiply vectors, where the answer is also a vector! I think the absolute easiest way to calculate the cross product is to cross in towers:
Rule
Don’t try to remember the letter combinations, that is really cumbersome and unnecessary. Rather, try to remember the pattern you follow when crossing the vectors. You will discover that forms a cross when you multiply like in the formula:
The same goes for :
And it also goes for :
Notice that the next cross begins with the variable that the last cross ended with. That means you only need to remember to begin in the middle and move towards the right. Make up two vectors and try the method out, you won’t regret it!
Rule
The cross product is perpendicular to both and .
If you use this formula, you can find the length of a cross product if you know the angle between the two vectors:
Formula
If you have the cross product as a vector, you can use the formula for vector length.
Example 1
Find the cross product of and . You get
Example 2
You have been given the vectors and , and the angle between them is . You know that and . How long is the cross product of the two vectors?
You insert the numbers into the formula, which gives you