Question

Find the magnitude and the direction of vactor C=3A - 2B, draw the three vectors in x-y system.

Answer 1

Since we already have the x and y components of vectors A and B, we just need to perform the equation for C in the two components.

x-component:
$C_{x}=3 A_{x}-2 B_{x} =3(-2)-2(2)=-6-4=-10$

y-component:
$C_{y}=3 A_{y}-2 B_{y} =3(4)-2(-5)=12+10=22$

We then solve for the magnitude of vector C by using the pythagorean theorem:

$C^{2}= C_{x}^{2}+C_{y}^{2}$
$C^{2}= (-10)^{2}+22^{2}=100+484=584$
$C=24.17$

For the direction, if we perform the operation $tan^{-1}(\frac{ C_{y}}{C_{x}})$, we'll get the angle from the horizontal.

$angle=tan^{-1}(\frac{22}{-10})=114.44deg$

ANSWER: Vector C has a magnitude of 24.17 N and a direction of 114.44 degrees from the horizontal.