Two unit vectors and in the plane make angles and with the positive -axis

MATHEMATICS · Subjective · CBSE · Mathematics · Vector Algebra · Vector Algebra

Problem

Two unit vectors

\mathbf{u}

and

\mathbf{v}

in the plane make angles

x

and

y

with the positive

x

-axis. Without performing any numerical calculation, explain why

\mathbf{u}\!\cdot\!\mathbf{v}=\cos(x-y)