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)(( C_(y))/(C_(x)))`, we'll get the angle from the horizontal.


`angle=tan^(-1)((22)/(-10))=114.44deg`

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