Question

If `A= <16 ,-4 ,-1 >` and `B= <2 ,-9 ,3 >`, what is `A*B -||A|| ||B||`?

Answer 1

`65-sqrt(25662) ≈ -95.19`

Explanation:

Since `A • B=x_1x_2+y_1y_2+z_1z_2`, the `A • B` term equals `(16*2) + (-4*-9) + (-1*3)`, which is 65.

Since the magnitude of a vector is given by `sqrt(x^2+y^2+z^2)`, the magnitude of A is `sqrt(16^2+(-4)^2+(-1)^2`, which equals `sqrt(273)`.

Likewise, the magnitude of B is `sqrt(2^2+(-9)^2+(3)^2`, which equals `sqrt(94)`

Therefore, the equation `A⋅B−||A||||B||` simplifies to `65-sqrt(273)*sqrt(94)` which further simplifies to `65-sqrt(25662)`, which is approximately -95.19