Science:Math Exam Resources/Courses/MATH152/April 2013/Question A 02/Solution 1

We will use the formula,

${\begin{aligned}{\text{Proj}}_{c}a&={\frac {a\cdot c}{|c|^{2}}}c.\end{aligned}}$

Note that

$a\cdot c=-9+12+36=39$

and

$|c|^{2}=c\cdot c=9+16+144=169.$

Hence,

${\begin{aligned}{\text{Proj}}_{c}a&={\frac {a\cdot c}{|c|^{2}}}c={\frac {39}{169}}c={\frac {3}{13}}{\begin{bmatrix}3\\-4\\12\end{bmatrix}}.\end{aligned}}$