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
