Question

Cross product of (2,4) x (-6,3) ?

Answer 1

Should be 30.

Explanation:

Cross products are usually done with 3-D vectors because they define the vector that is perpendicular to the first two; therefore we need to re-write these in 3D form. Since we know they only exist in the x-y plane, the z value is always 0.

`a=[2, 4, 0]`
`b=[-6, 3, 0]`

Then we take the cross product for the three dimensions
`a ox b =(4*0-0*3)hati+(0*(-6)-(2*0))hatj+(2*3-4*(-6))hatk`

`a ox b =0hati+0hatj+(6-(-24))hatk`

`a ox b =0hati+0hatj+30hatk`

You can see that the perpendicular vector will be purely in the z-axis (our cross product). This makes sense because the first two vectors are purely in the x-y plane. Since we only have one number, the answer is `color(red)30`. If it is needed in coordinate form, it would be `color(red)([0, 0, 30]`