Question

If `A= <2 ,-3 ,-4 >` and `B= <-1, -4, 2 >`, what is `A*B -||A|| ||B||`?

Answer 1

`2-sqrt(609) ≈ -22.68`

Explanation:

Since `A • B=x_1x_2+y_1y_2+z_1z_2`, the `A • B` term equals `(2*-1) + (-3*-4) + (-4*2)`, which is 2.

Since the magnitude of a vector is given by `sqrt(x^2+y^2+z^2)`, the magnitude of A is `sqrt(2^2+(-3)^2+(-4)^2`, which equals `sqrt(29)`.

Likewise, the magnitude of B is `sqrt((-1)^2+(-4)^2+2^2`, which equals `sqrt(21)`

Therefore, the equation `A⋅B−||A||||B||` simplifies to `2-sqrt(29)*sqrt(21)` which further simplifies to `2-sqrt(609)`, which is approximately -22.68