# What is the cross product of #[3,2, 5]# and #[2, -5, 8] #?

##### 1 Answer

By hand and then checked with MATLAB: [41 -14 -19]

#### Explanation:

When you take a cross product, I feel like it makes things easier to add in the unit vector directions

We'll use all three since these are 3-D vectors that we're dealing with. If it was 2d you'd only have to use

Now we set up a 3x3 matrix as follows (Socratic doesn't give me a good way to do multidimensional matrices, sorry!):

Now, starting at each unit vector, go diagonal from left to right, taking the product of those numbers:

Next, take the products of the values going from right to left; again, starting at the unit vector:

Finally, take the first set and subtract the second set from it

this can now be re-written in matrix form, with