If vectors and are non-collinear

MATHEMATICS · Single correct · CBSE · Mathematics · Vector Algebra · Vector Algebra

Problem

If vectors

\mathbf{a}

and

\mathbf{b}

are non-collinear, then

\frac{\mathbf{a}}{|\mathbf{a}|} + \frac{\mathbf{b}}{|\mathbf{b}|}

is (1) a unit vector (2) in the plane of

\mathbf{a}

and

\mathbf{b}

(3) equally inclined to

\mathbf{a}

and

\mathbf{b}

(4) perpendicular to

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