Question

The vectors are given by $\hat{A}=\hat{i}+2\hat{j}+2\hat{k}$ and $\hat{B}=3\hat{i}+6\hat{j}+2\hat{k}$. Another vector $\overrightarrow{C}$ has the same magnitude as $B$ but has the same direction as $A$. Then which of the following vectors represents $\overrightarrow{C}$?

• A. $\frac{7}{3}(\hat{i}+2\hat{j}+2\hat{k})$
• B. $\frac{3}{7}(\hat{i}-2\hat{j}+2\hat{k})$
• C. $\frac{7}{9}(\hat{i}-2\hat{j}+2\hat{k})$
• D. $\frac{9}{7}(\hat{i}+2\hat{j}+2\hat{k})$

Answer 1

The correct option is A $\frac{7}{3}(\hat{i}+2\hat{j}+2\hat{k})$

Given: $\hat{A}=\hat{i}+2\hat{j}+2\hat{k}$ and $\hat{B}=3\hat{i}+6\hat{j}+2\hat{k}$

So, $\overrightarrow{C}=\frac{\hat{i}+2\hat{j}+2\hat{k}}{\sqrt{1+4+4}}\times \sqrt{3^2+6^2+2^2}$

$=\frac{\hat{i}+2\hat{j}+2\hat{k}}{3}\times \sqrt{49}=\frac{7}{3}(\hat{i}+2\hat{j}+2\hat{k})$