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

Answer:

$v=$

Explanation:

We are given that

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

v lies in the first quadrant

$\theta=\frac{\pi}{3}$

$v_x=\mid v\mid cos\theta$

$v_y=\mid v\mid sin\theta$

Substitute the values then we get

$v_x=4cos\frac{\pi}{3}$

$v_x=4\times \frac{1}{2}=2$

$cos\frac{\pi}{3}=\frac{1}{2}$

$v_y=4\times sin\frac{\pi}{3}=4\times \frac{\sqrt 3}{2}=2\sqrt 3$

$sin\frac{\pi}{3}=\frac{\sqrt 3}{2}$

Therefore, the vector v in component form$=$

$v=$