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

We will use the formula,

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

Note that

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

and

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

Hence,

$\begin{array}{rl}{\text{Proj}}_{c}a& =\frac{a\cdot c}{|c{|}^2}c=\frac{39}{169}c=\frac{3}{13}\left[\begin{array}{c}3\\ -4\\ 12\end{array}\right].\end{array}$