Question

Vector u has initial point at (4, 4) and terminal point at (–12, 8). Which are the magnitude and direction of u?

Answer 1

Let's find the magnitude of each component:

Let:

$\begin{gathered} (x1,y1)=(4,4) \\ (x2,y2)=(-12,8) \\ \vec{u}=ax+by \\ \mleft\Vert\vec{u}\mright||=\sqrt[]{a^2+b^2} \end{gathered}$

So, let's find a and b:

$\begin{gathered} a=|x2-x1|=|-12-4|=|-16|=16 \\ b=|y2-y1|=|8-4|=|4|=4 \end{gathered}$

so:

$\begin{gathered} \Vert\vec{u}||=\sqrt[]{16^2+4^2} \\ \Vert\vec{u}||=\sqrt[]{272} \\ \Vert\vec{u}||\approx16.492 \end{gathered}$

And the direction is:

$\begin{gathered} \theta=180-\tan ^{-1}(\frac{b}{a}) \\ \theta=180-\tan ^{-1}(\frac{4}{16}) \\ \theta\approx180-\tan ^{-1}(\frac{4}{16})\approx165.963 \end{gathered}$