# If A= <-3 ,4 ,-1 > and B= <8 ,-4 ,2 >, what is A*B?

Mar 1, 2016

$- 42$

#### Explanation:

given 2 vectors  ula = (x_1,y_1,z_1) " and ulb=(x_2,y_2,z_2)

then $\underline{a} . \underline{b} = \left({x}_{1} \times {x}_{2}\right) + \left({y}_{1} \times {y}_{2}\right) + \left({z}_{1} \times {z}_{2}\right)$

here $A = \left({x}_{1} , {y}_{1} , {z}_{1}\right) = \left(- 3 , 4 , - 1\right)$

and $B = \left({x}_{2} , {y}_{2} , {z}_{2}\right) = \left(8 , - 4 , 2\right)$

$\Rightarrow A . B = \left(- 3 \times 8\right) + \left(4 \times - 4\right) + \left(- 1 \times 2\right)$

= - 24 - 16 - 2 = - 42