Question

If `A= <-3 ,3 ,-1 >` and `B= <8 ,7 ,2 >`, what is `A*B -||A|| ||B||`?

Answer 1

`-5-sqrt(2223) ≈ -52.15`

Explanation:

Since `A • B=x_1x_2+y_1y_2+z_1z_2`, the `A • B` term equals `(-3*8) + (3*7) + (-1*2)`, which is -5.

Since the magnitude of a vector is given by `sqrt(x^2+y^2+z^2)`, the magnitude of A is `sqrt((-3)^2+(3)^2+(-1)^2`, which equals `sqrt(19)`.

Likewise, the magnitude of B is `sqrt(8^2+7^2+2^2`, which equals `sqrt(117)`

Therefore, the equation `A⋅B−||A||||B||` simplifies to `-5-sqrt(19)*sqrt(117)` which further simplifies to `-5-sqrt(2223)`, which is approximately -52.15