Mathematics

Problem

Let the unit vectors

\mathbf{a}

and

\mathbf{b}

be perpendicular and unit vector

\mathbf{c}

is inclined at angle

\alpha

\mathbf{a}

and

\mathbf{b}

. If

\mathbf{c} = l\mathbf{a} + m\mathbf{b} + n(\mathbf{a} \times \mathbf{b})

, then a.

l = m

n^2 = 1 - 2l^2

n^2 = -\cos 2\alpha

m^2 = \frac{1 + \cos 2\alpha}{2}