# How do you find the cross product and state whether the resulting vectors are perpendicular to the given vectors #<-1,-3,2>times<6,-1,-2>#?

##### 1 Answer

The cross product of two vectors will always result in a third vector that is perpendicular to both. You can check that is it perpendicular by verifying that the dot-product with either vector is zero.

#### Explanation:

I use a 5 column determinant to compute the cross-product:

Add the product of the diagonal descending to the right and subtract the product of the diagonal descending to the left.

Simplify:

Convert the vector notation:

Verify that it is perpendicular to the first vector:

The dot-product is 0, therefore, the two vectors are perpendicular.

Verify that it is perpendicular to the second vector:

The dot-product is 0, therefore, the two vectors are perpendicular.