Question

If `A= <8 ,- 2 ,9>` and `B= <5 ,1 ,0 >`, what is `A*B -||A|| ||B||`?

Answer 1

`65-sqrt(3874) ≈ 2.76`

Explanation:

Since `A • B=x_1x_2+y_1y_2+z_1z_2`, the `A • B` term equals `(8*5) + (-2*1) + (9*0)`, which is 38.

Since the magnitude of a vector is given by `sqrt(x^2+y^2+z^2)`, the magnitude of A is `sqrt(8^2+(-2)^2+9^2`, which equals `sqrt(149)`.

Likewise, the magnitude of B is `sqrt(5^2+1^2+0^2`, which equals `sqrt(26)`

Therefore, the equation `A⋅B−||A||||B||` simplifies to `38-sqrt(149)*sqrt(26)` which further simplifies to `65-sqrt(3874)`, which is approximately 2.76