Mathematics

Problem

Let

\mathbf{a}

\mathbf{b}

and

\mathbf{c}

be three non-coplanar vectors and

\mathbf{d}

be a non-zero vector, which is perpendicular to

\mathbf{a} + \mathbf{b} + \mathbf{c}

. Now, if

\mathbf{d} = (\sin x)(\mathbf{a} \times \mathbf{b}) + (\cos y)(\mathbf{b} \times \mathbf{c}) + 2(\mathbf{c} \times \mathbf{a})

, then minimum value of

x^2 + y^2

is equal to a.

\pi^2

\frac{\pi^2}{2}

\frac{\pi^2}{4}

\frac{5\pi^2}{4}