Question

Find the direction cosines of the vector $\overrightarrow{a}=\hat{i}+\hat{j}-2\hat{k}$.

• A. $(\frac{1}{\sqrt{6}},\frac{1}{\sqrt{6}},-\frac{2}{\sqrt{6}})$
• B. $(\frac{1}{\sqrt{3}},\frac{1}{\sqrt{6}},\frac{-2}{\sqrt{6}})$
• C. $(\frac{1}{\sqrt{6}},\frac{1}{\sqrt{6}},\frac{-2}{\sqrt{3}})$
• D. None of these

Answer 1

The correct option is A $(\frac{1}{\sqrt{6}},\frac{1}{\sqrt{6}},-\frac{2}{\sqrt{6}})$

$\overrightarrow{a}=i+j-2k$
Or
$\frac{\overrightarrow{a}}{a}=\frac{i+j-2k}{\sqrt{6}}=\frac{i}{\sqrt{6}}+\frac{j}{\sqrt{6}}-\frac{2k}{\sqrt{6}}$
Hence the respective direction co-sines are
$(\frac{1}{\sqrt{6}},\frac{1}{\sqrt{6}},-\frac{2}{\sqrt{6}})$