# Given the vectors u=<2,2>, v=<-3,4>, and w=<1,-2>, how do you find (v*u)w?

Jun 29, 2016

$\left(v \cdot u\right) w = < 2 , - 4 >$

#### Explanation:

As $u = < 2 , 2 >$ and $v = < - 3 , 4 >$,

their dot product $v \cdot u = \left[\left(- 3\right) \times 2 + 4 \times 2\right] = \left[- 6 + 8\right] = 2$,, which is a scalar.

Hence as $w = < 1 , - 2 >$, $\left(v \cdot u\right) w$ is a product of a scalar and vector and hence a vector and is given by

$\left(v \cdot u\right) w = 2 < 1 , - 2 > = < 2 , - 4 >$