Let and . The resultant vector satisfies . (a) Determine the value(s) of that satisfy…

MATHEMATICS · Subjective · CBSE · Mathematics · Vector Algebra · Vector Algebra

Problem

Let

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

and

\mathbf{q}=4\hat{i}-\hat{j}+5\hat{k}

. The resultant vector

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

satisfies

|\mathbf{r}|=7

. (a) Determine the value(s) of

x

that satisfy this condition. (b) Using the value of

x

obtained, write

\mathbf{r}

in component form. (c) Find the unit vector in the direction of

\mathbf{r}