Question

If the direction of cosines of a vector are $\frac{3}{5\sqrt{2}},\frac{4}{5\sqrt{2}}$ and $\frac{1}{\sqrt{2}}$ respectively, then the vector is:

• A. $3\hat{i}+4\hat{j}+\hat{k}$
• B. $3\hat{i}+4\hat{j}+\sqrt{5}\hat{k}$
• C. $3\sqrt{2}\hat{i}+4\sqrt{2}\hat{j}+\hat{k}$
• D. $3\hat{i}+4\hat{j}+5\hat{k}$

Answer 1

The correct option is A $3\hat{i}+4\hat{j}+\hat{k}$

Given, the direction cosines,

$(\frac{a}{|a|},\frac{b}{|b|},\frac{c}{|c|})=(\frac{3}{5\sqrt{2}},\frac{4}{5\sqrt{2}},\frac{1}{\sqrt{2}})$

Then the direction ratios, $(a,b,c)=(3,4,1)$

We know equation of a vector, $\overrightarrow{v}=a\hat{i}+b\hat{j}+c\hat{k}$

Then the vector with given direction ratios will be $\overrightarrow{v}=3\hat{i}+4\hat{j}+\hat{k}$