Mathematics

Problem

If vectors

\mathbf{a}

and

\mathbf{b}

are two adjacent sides of a parallelogram, then the vector representing the altitude of the parallelogram which is perpendicular to

\mathbf{a}

is a.

\mathbf{b} + \frac{\mathbf{b} \times \mathbf{a}}{|\mathbf{a}|^2}

\frac{\mathbf{a} \cdot \mathbf{b}}{|\mathbf{b}|^2} \mathbf{b}

\mathbf{b} - \frac{\mathbf{b} \cdot \mathbf{a}}{|\mathbf{a}|^2} \mathbf{a}

\frac{\mathbf{a} \times (\mathbf{b} \times \mathbf{a})}{|\mathbf{a}|^2}