Question

If `A= <-8 ,3 ,-1 >` and `B= <-3 ,4 ,3 >`, what is `A*B -||A|| ||B||`?

Answer 1

`33-sqrt(2516) ≈ -17.16`

Explanation:

Since `A • B=x_1x_2+y_1y_2+z_1z_2`, the `A • B` term equals `(-8*-3) + (3*4) + (-1*3)`, which is 33.

Since the magnitude of a vector is given by `sqrt(x^2+y^2+z^2)`, the magnitude of A is `sqrt((-8)^2+3^2+(-1)^2`, which equals `sqrt(74)`.

Likewise, the magnitude of B is `sqrt((-3)^2+4^2+3^2`, which equals `sqrt(34)`

Therefore, the equation `A⋅B−||A||||B||` simplifies to `33-sqrt(74)*sqrt(34)` which further simplifies to `33-sqrt(2516)`, which is approximately -17.16