Given three vectors

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

Problem

Given three vectors

\mathbf{a} = 6\hat{i} - 3\hat{j}

\mathbf{b} = 2\hat{i} - 6\hat{j}

and

\mathbf{c} = -2\hat{i} + 21\hat{j}

such that

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

. Then, the resolution of the vector

\alpha

into components with respect to

\mathbf{a}

and

\mathbf{b}

is given by (1)

3\mathbf{a} - 2\mathbf{b}

(2)

3\mathbf{b} - 2\mathbf{a}

(3)

2\mathbf{a} - 3\mathbf{b}

(4)

\mathbf{a} - 2\mathbf{b}