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

D- ||u|| = 16.492; θ = 165.964°

Explanation:

I took the quiz

Answer 2

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