Question

The vector of magnitude $3\sqrt{21}$ in the direction of vector $(4,1,-2)$ is _______

• A. $(-12,-3,6)$
• B. $\frac{1}{\sqrt{21}}(12,3,-6)$
• C. $(12,3,-6)$
• D. $\frac{1}{\sqrt{21}}(4,1,-2)$

Answer 1

Answer: (C)

$(12,3,-6)$

Vector in direction of $(4,1,-2)=4\overrightarrow{i}+\overrightarrow{j}-2\overrightarrow{k}$

As $\sqrt{(4{)}^2+(1{)}^2+(-2{)}^2}=\sqrt{21}$

So

Unit vector in direction of $(4,1,-2)=\frac{4\overrightarrow{i}}{\sqrt{21}}+\frac{\overrightarrow{j}}{\sqrt{21}}-\frac{2\overrightarrow{k}}{\sqrt{21}}$

Vector in direction of $(4,1,-2)$ with magnitude $3\sqrt{21}=3\sqrt{21}(\frac{4\overrightarrow{i}}{\sqrt{21}}+\frac{\overrightarrow{j}}{\sqrt{21}}-\frac{2\overrightarrow{k}}{\sqrt{21}})=12\overrightarrow{i}+3\overrightarrow{j}-6\overrightarrow{k}$