Question

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

||u|| = 14.422; θ = 33.690°
||u|| = 14.422; θ = 146.310°
||u|| = 16.492; θ = 14.036°
||u|| = 16.492; θ = 165.964°

Answer 1

Let's find the magnitude of each component:

Let:

`(x1,y1)=(4,4)`

`(x2,y2)=(-12,8)`

`u=ax+by`

`||u||=√(a^2+b^2)`

So, let's find a and b:

`a=|x2-x1|=|-12-4|=|-16|=16`

`b=|y2-y1|=|8-4|=|4|=4`

so:

`||u||=√(16^2+4^2)`

`||u||=√(272)`

`||u||\thickapprox16.492`

And the direction is:

`\theta=180-\text{tan}^(-1)\huge \text((b)/(a)\huge \text)`

`\theta=180-\text{tan}^(-1)\huge \text((4)/(16)\huge \text)`

`\theta\thickapprox180-\text{tan}^(-1)\huge \text((4)/(16)\huge \text)\thickapprox165.964`