# If A= <4, 3 ,-1 > and B= <9 ,7 ,6 >, what is A*B -||A|| ||B||?

$51 - 2 \sqrt[2]{1079}$
The scalar product is $\left(4 , 3 , - 1\right) \cdot \left(9 , 7 , 6\right) = 4 \cdot 9 + 3 \cdot 7 - 1 \cdot 6 = 51$
$A = \sqrt[2]{{4}^{2} + {3}^{2} + {\left(- 1\right)}^{2}} = \sqrt[2]{26}$
$B = \sqrt[2]{{9}^{2} + {7}^{2} + {6}^{2}} = \sqrt[2]{166}$