Given the vectors

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

Problem

Given the vectors

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

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

and

\mathbf{c}=5\hat{i}+2\hat{j}+4\hat{k}

, find the vector

\mathbf{r}=2\mathbf{a}-\mathbf{b}+\mathbf{c}

in unit-vector form. Also calculate

|\mathbf{r}|