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

Vector $\overset{\rightarrow}{A} = 3i - 4j + 5k$. We know that direction cosines of

$\overset{\rightarrow}{A} = \frac{3}{\sqrt{3^{2} + 4^{2} + 5^{2}}},\frac{- 4}{\sqrt{3^{2} + 4^{2} + 5^{2}}},\frac{5}{\sqrt{3^{2} + 4^{2} + 5^{2}}}$

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