Question

If v lies in the first quadrant and makes an angle Ï/3 with the positive x-axis and |v| = 4, find v in component form.

Answer 1

`v=<2,2\sqrt 3>`

Step-by-step explanation:

We are given that

Magnitude of vector v=
`\mid v\mid =4`

v lies in the first quadrant

`\theta=(\pi)/(3)`

`v_x=\mid v\mid cos\theta`

`v_y=\mid v\mid sin\theta`

Substitute the values then we get

`v_x=4cos(\pi)/(3)`

`v_x=4* (1)/(2)=2`

`cos(\pi)/(3)=(1)/(2)`

`v_y=4* sin(\pi)/(3)=4* (\sqrt 3)/(2)=2\sqrt 3`

`sin(\pi)/(3)=(\sqrt 3)/(2)`

Therefore, the vector v in component form
`=<v_x,v_y>`

`v=<2,2\sqrt 3>`