What is the projection of <4,9,1 > onto <-1,7,2 >?

Apr 7, 2016

$\frac{61}{\sqrt{54}}$

Explanation:

$\vec{A} = \left\{4 , 9 , 1\right\}$ and $\vec{B} = \left\{- 1 , 7 , 2\right\}$

Projection of $\vec{A}$ on $\vec{B}$ is the dot product of $\vec{A}$ and unit vector $\vec{B}$.

Hence;
$\vec{A} \cdot \hat{B}$
$= \vec{A} \cdot \frac{\vec{B}}{| \vec{B} |}$
$= \left\{4 , 9 , 1\right\} . \frac{\left\{- 1 , 7 , 2\right\}}{\sqrt{{1}^{2} + {7}^{2} + {2}^{2}}}$
$= \frac{4 \cdot \left(- 1\right) + 9 \cdot 7 + 1 \cdot 2}{\sqrt{54}}$
$= \frac{61}{\sqrt{54}}$