# What is the projection of  (-9 i + j + 2 k) onto (-5i + 12j- 5 k)?

Sep 27, 2017

Let

vecA=−9hati+hatj+3hatk

and

vecB=−5hati+12hatj-5hatk

Now projection of $\vec{A}$ onto $\vec{B}$

$= \frac{\vec{A} \cdot \vec{B}}{\left\mid \vec{B} \right\mid} ^ 2 \vec{B}$

$= \frac{45 + 12 - 15}{\sqrt{{5}^{2} + {12}^{2} + {5}^{2}}} ^ 2 \left(- 5 \hat{i} + 12 \hat{j} - 5 \hat{k}\right)$

$= \frac{21}{97} \left(- 5 \hat{i} + 12 \hat{j} - 5 \hat{k}\right)$