How do I find the component form of a vector, given magnitude and angle?

Question

For example: ||v|| = 9sqrt3 when drawn in standard position and makes a 60deg angle with the negative x-axis, and lies in quadrant 3

Answer 1

x = 9√3cos120° = - 9√3·1/2 = - 9√3/2; y = 9√3sin120° = 27/2.

So, vector: <- 9√3/2, 27/2> = - 9√3/2i + 27/2j