Question

If the angle between 2 vectors of equal magnitude P is theta,then the magnitude of the difference vector is?

Answer 1

Vectors A and B are of magnitude P inclined at an angle θ .

$| \vec{a} \: - \vec{b}|^{2} = {p}^{2} + {p}^{2} - 2 \: p \: p \: cos \theta \\ = 2{p}^{2} (1 - cos \theta) = 4 \: {p}^{2} {sin}^{2} \frac{ \theta}{2} \\ \\ answer = 2 p \: sin \frac{ \theta}{2}$