Question

How do you find the area of the parallelogram with vertices: p(0,0,0), q(-5,0,4), r(-5,1,2), s(-10,1,6)?

Answer 1

`sqrt141`?

Explanation:

The area of a parallelogram is the magnitude of the cross-product of any two non-parallel sides.
Take `vec(PQ)` and `vec(PR)`, say, because they share a point and so can't be parallel:
`||(hat (i),hat j,hat k),(-5,0,4),(-5,1,2)||`
`=sqrt(16+100+25)`
=`sqrt141` (if my vector multiplication and scalar multiplication are correct!)