Unit vector along the direction of vector $\vec{a}$ , $\vec{a}$ = $\frac{\vec{a}}{|\vec{a}|}$ Let $\vec{a}$ = $\hat{i} - 2\hat{j} + 2\hat{k}$ $|\vec{a}|$ = $\sqrt{(1)^2+(-2)^2+(2)^2}$ = ± 3 i.e. $\hat{a}$ = $\frac{1}{3}(\hat{i} - 2\hat{j} + 2\hat{k})$ So, the vector whose magnitude is 15 and has direction along the vector $\hat{i} - 2\hat{j} + 2\hat{k}$ is given by, 15 × $\left(\frac{1}{3}\right)\left(\hat{i} - 2\hat{j} + 2\hat{k}\right)$ = 5 $\left(\hat{i} - 2\hat{j} + 2\hat{k}\right)$ = $\left(5\hat{i} - 10\hat{j} + 10\hat{k}\right)$ So the required vector is $\left(5\hat{i} - 10\hat{j} + 10\hat{k}\right)$