Question

The direction cosines of a vector $\hat{i}+\hat{j}+\sqrt{2}\hat{k}$ are

• A. $\frac{1}{2},\frac{1}{2},1$
• B. $\frac{1}{\sqrt{2}},\frac{1}{\sqrt{2}},\frac{1}{2}$
• C. $\frac{1}{2},\frac{1}{2},\frac{1}{\sqrt{2}}$
• D. $\frac{1}{\sqrt{2}},\frac{1}{\sqrt{2}},\frac{1}{\sqrt{2}}$

Answer 1

Answer: (C)

$\frac{1}{2},\frac{1}{2},\frac{1}{\sqrt{2}}$

Direction cosine of $a\hat{i}+b\hat{j}+c\hat{k}$ can be given as $\frac{a}{\sqrt{a^2+b^2+c^2}},\frac{b}{\sqrt{a^2+b^2+c^2}}\frac{c}{\sqrt{a^2+b^2+c^2}}$
Thus, here we have directional cosines as $\frac{1}{\sqrt{1^2+1^2+(\sqrt{2}{)}^2}},\frac{1}{\sqrt{1^2+1^2+(\sqrt{2}{)}^2}},\frac{\sqrt{2}}{\sqrt{1^2+1^2+(\sqrt{2}{)}^2}}$
=$\frac{1}{2},\frac{1}{2},\frac{1}{\sqrt{2}}$