Mathematics

Problem

For non-zero vectors

\mathbf{u}

and

\mathbf{v}

making an angle

\theta

, which of the following correctly gives

\cos\theta

in terms of

\mathbf{u}

and

\mathbf{v}

? a)

\displaystyle \frac{|\mathbf u|\,|\mathbf v|}{\mathbf u\cdot \mathbf v}

\displaystyle \frac{\mathbf u\cdot \mathbf v}{\,|\mathbf u|\,|\mathbf v|\,}

\displaystyle \frac{\mathbf u\cdot \mathbf v}{|\mathbf u|^{2}+|\mathbf v|^{2}}

\displaystyle \frac{|\mathbf u|^{2}+|\mathbf v|^{2}-|\mathbf u-\mathbf v|^{2}}{|\mathbf u|\,|\mathbf v|}