Question

The direction cosines of the vector $3\mathbf{i} - 4\mathbf{j} + 5\mathbf{k}$ are

• A. $\frac{3}{5},\frac{- 4}{5},\frac{1}{5}$
• B. $\frac{3}{5\sqrt{2}},\frac{- 4}{5\sqrt{2}},\frac{1}{\sqrt{2}}$
• C. $\frac{3}{\sqrt{2}},\frac{- 4}{\sqrt{2}},\frac{1}{\sqrt{2}}$
• D. $\frac{3}{5\sqrt{2}},\frac{4}{5\sqrt{2}},\frac{1}{\sqrt{2}}$

Answer 1

Answer: (B)

$\frac{3}{5\sqrt{2}},\frac{- 4}{5\sqrt{2}},\frac{1}{\sqrt{2}}$

Answer 2

$\mathbf{r} = 3\mathbf{i} - 4\mathbf{j} + 5\mathbf{k}$; $|\mathbf{r}| = \sqrt{3^{2} + ( - 4)^{2} + 5^{2}} = 5\sqrt{2}$

Hence, direction cosines are $\frac{3}{5\sqrt{2}},\frac{- 4}{5\sqrt{2}},\frac{5}{5\sqrt{2}}$ i.e., $\frac{3}{5\sqrt{2}},\frac{- 4}{5\sqrt{2}},\frac{1}{\sqrt{2}}$