Let , and be three vectors. A vector in the plane of and , whose projection on is ,…

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

Problem

Let

\vec{a} = \hat{i} + \hat{j} + \hat{k}

\vec{b} = \hat{i} - \hat{j} + \hat{k}

and

\vec{c} = \hat{i} - \hat{j} - \hat{k}

be three vectors. A vector

\vec{v}

in the plane of

\vec{a}

and

\vec{b}

, whose projection on

\vec{c}

\frac{1}{\sqrt{3}}

, is given by (1)

\hat{i} - 3\hat{j} + 3\hat{k}

(2)

-3\hat{i} - 3\hat{j} - \hat{k}

(3)

3\hat{i} - \hat{j} + 3\hat{k}

(4)

\hat{i} + 3\hat{j} - 3\hat{k}