Question

Determine the projection of u=1.6i+3.3j in the v=-2.1i-0.5j direction

Answer 1

The projection of $\vec u$ onto $\vec v$ is

$\mathrm{proj}_{\vec v}(\vec u)=\dfrac{\vec u\cdot\vec v}{\vec v\cdot\vec v}\vec v$

We have

$\vec u\cdot\vec v=1.6\cdot(-2.1)+3.3\cdot(-0.5)=-5.01$

$\vec v\cdot\vec v=\|\vec v\|^2=(-2.1)^2+(-0.5)^2=4.66$

$\implies\mathrm{proj}_{\vec v}(\vec u)=\dfrac{-5.01}{4.66}\vec v\approx2.26\,\vec\imath+0.54\,\vec\jmath$