Question

The direction cosines of a vector A are $\cos \alpha =\frac{4}{5\sqrt{2}},$ $cos\beta =\frac{1}{\sqrt{2}},$ and $cos\gamma =\frac{3}{5\sqrt{2}},$ then vector A is

• A. $4i+j+3k$
• B. $4i+5j+3k$
• C. 4i-5j-3k
• D. none

Answer 1

The correct option is A $4i+j+3k$

$\overrightarrow{A}=a\hat{i}+b\hat{j}+c\hat{k}$

$\cos \alpha =\frac{a}{\sqrt{a^2+b^2+c^2}}$ $\cos \beta =\frac{b}{\sqrt{a^2+b^2+c^2}}$ $\cos \gamma =\frac{c}{\sqrt{a^2+b^2+c^2}}$

$\sqrt{4^2+5^2+3^2}=\sqrt{16+25+9}=\sqrt{50}=5\sqrt{2}$

$\overrightarrow{A}=4\hat{i}+5\hat{j}+3\hat{k}$