If unit vectors and are at right angles to each other and ,

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

Problem

If unit vectors

\hat{i}

and

\hat{j}

are at right angles to each other and

\mathbf{p} = 3\hat{i} + 4\hat{j}

\mathbf{q} = 5\hat{i}

4\mathbf{r} = \mathbf{p} + \mathbf{q}

and

2\mathbf{s} = \mathbf{p} - \mathbf{q}

, then (1)

|\mathbf{r} + k\mathbf{s}| = |\mathbf{r} - k\mathbf{s}| \text{ for all real } k

(2)

\mathbf{r} \text{ is perpendicular to } \mathbf{s}

(3)

\mathbf{r} + \mathbf{s} \text{ is perpendicular to } \mathbf{r} - \mathbf{s}

(4)

|\mathbf{r}| = |\mathbf{s}| = |\mathbf{p}| = |\mathbf{q}|