Mathematics

Problem

Statement I The number of vectors of unit length and perpendicular to both the vectors

\hat{i} + \hat{j}

and

\hat{j} + \hat{k}

is zero. Statement II

\mathbf{a}

and

\mathbf{b}

are two non-zero and non-parallel vectors it is true that

\mathbf{a} \times \mathbf{b}

is perpendicular to the plane containing

\mathbf{a}

and

\mathbf{b}