Find the component form of v given its magnitude and the angle it makes with the positive x-axis. Magnitude: ||v||=2 √15 Angle : θ = 45°

Answer 1

The component parts of a vector are r cos theta and r sin theta. where r is ||v|| or magnitude and theta is the angle.

45 degrees is the angle in a special 45, 45 right triangle. The sin 45 = cos 45 = sqrt(2)/2

Thus both components are (2sqrt(15)) (sqrt(2)/2) = sqrt(30)