# How do you find the inner product and state whether the vectors are perpendicular given <3,4,0>*<4,-3,6>?

Feb 11, 2017

The inner product is $= 0$

#### Explanation:

The dot product or inner product of 2 vectors $\vec{a}$ and $\vec{b}$ is

veca.vecb=〈a_1,a_2,a_3〉.〈b_1,b_2,b_3〉=a_1b_1+a_2b_2+a_3b_3

Here,

$\vec{a} = < 3 , 4 , 0 >$

$\vec{b} = < 4 , - 3 , 6 >$

The inner product is

$< 3 , 4 , 0 > . < 4 , 3 , - 6 > = 3 \cdot 4 - 4 \cdot 3 + 0 = 12 - 12 = 0$

As the inner product is $= 0$, the 2 vectors are perpendicular