Answer:
[tex]v=<2,2\sqrt 3>[/tex]
Explanation:
We are given that
Magnitude of vector v=[tex]\mid v\mid =4[/tex]
v lies in the first quadrant
[tex]\theta=\frac{\pi}{3}[/tex]
[tex]v_x=\mid v\mid cos\theta[/tex]
[tex]v_y=\mid v\mid sin\theta[/tex]
Substitute the values then we get
[tex]v_x=4cos\frac{\pi}{3}[/tex]
[tex]v_x=4\times \frac{1}{2}=2[/tex]
[tex]cos\frac{\pi}{3}=\frac{1}{2}[/tex]
[tex]v_y=4\times sin\frac{\pi}{3}=4\times \frac{\sqrt 3}{2}=2\sqrt 3[/tex]
[tex]sin\frac{\pi}{3}=\frac{\sqrt 3}{2}[/tex]
Therefore, the vector v in component form[tex]=<v_x,v_y>[/tex]
[tex]v=<2,2\sqrt 3>[/tex]
