Question

Direction cosines of the vector $\overline{v}=a_1\hat{i}+a_2\hat{j}+a_3\hat{k}$ are

• A. $<a_1,a_2,a_3>$
• B. $<-a_1,-a_2,-a_3>$
• C. $<\frac{a_1}{\left|\overline{v}\right|},\frac{a_2}{\left|\overline{v}\right|,}\frac{a_3}{\left|\overline{v}\right|},>$
• D. none of these

Answer 1

The correct option is C $<\frac{a_1}{\left|\overline{v}\right|},\frac{a_2}{\left|\overline{v}\right|,}\frac{a_3}{\left|\overline{v}\right|},>$

The directions cosines will be
$\frac{a_1}{\sqrt{a_1^2+a_2^2+a_3^2}},\frac{a_2}{\sqrt{a_1^2+a_2^2+a_3^2}},\frac{a_3}{\sqrt{a_1^2+a_2^2+a_3^2}}$
$\Rightarrow \frac{a_1}{|\overline{v}|},\frac{a_2}{|\overline{v}|},\frac{a_3}{|\overline{v}|}$