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

Feb 6, 2016

-5-sqrt(2223) ≈ -52.15

#### Explanation:

Since A • B=x_1x_2+y_1y_2+z_1z_2, the A • B term equals $\left(- 3 \cdot 8\right) + \left(3 \cdot 7\right) + \left(- 1 \cdot 2\right)$, 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 $- 5 - \sqrt{19} \cdot \sqrt{117}$ which further simplifies to $- 5 - \sqrt{2223}$, which is approximately -52.15