Vectors and together with an unknown vector satisfy .

MATHEMATICS · Multi-part · CBSE · Mathematics · Vector Algebra · Vector Algebra

Problem

Vectors

\mathbf{p}=2\hat{i}+3\hat{j}+6\hat{k}

and

\mathbf{q}=-4\hat{i}+7\hat{j}-2\hat{k}

together with an unknown vector

\mathbf{r}

satisfy

\mathbf{p}+\mathbf{q}+\mathbf{r}=\mathbf{0}

. (a) Determine the components of

\mathbf{r}

. (b) Find the magnitude of

\mathbf{r}

. (c) Calculate the direction cosines of

\mathbf{r}

. (d) Prove that the squares of the direction cosines obtained in part (c) add up to

1