# How do I find the cross product of <-13, 4> and <-56, 0>?

Jan 23, 2015

You have two options to evaluate the cross product:
1) the cross product of two vectors $\vec{v}$ and $\vec{w}$ is a vector with modulus equal to|vecv|×|vecw|×sin(theta) ($\theta$ is the angle between the vectors), direction perpendicular to the plane formed by the two vectors and oriented using the "thumb of the right hand" rule;
2) evaluate the determinant:

In your case I would use the second option and use the first to check the result. So:

So basically, the result is a vector in the positive $z$ direction and modulus 224, or:
$< 0 , 0 , 224 >$

Using the first approach you get the same result considering:

Try to evaluate the modulus (using |vecv|×|vecw|×sin(theta)) and consider the direction of the resulting vector you'll see that it matches.