Question

If $\overset{\rightarrow}{A} = 2\widehat{i} + 4\widehat{j} - 5\widehat{k}$ the direction of cosines of the vector $\overset{\rightarrow}{A}$ are

• A. $\frac{2}{\sqrt{45}},\frac{4}{\sqrt{45}}\text{and}\frac{- 5}{\sqrt{\text{45}}}$
• B. $\frac{1}{\sqrt{45}},\frac{2}{\sqrt{45}}\text{and}\frac{3}{\sqrt{\text{45}}}$
• C. $\frac{4}{\sqrt{45}},0\text{and}\frac{4}{\sqrt{45}}$
• D. $\frac{3}{\sqrt{45}},\frac{2}{\sqrt{45}}\text{and}\frac{5}{\sqrt{\text{45}}}$

Answer 1

Answer: (A)

$\frac{2}{\sqrt{45}},\frac{4}{\sqrt{45}}\text{and}\frac{- 5}{\sqrt{\text{45}}}$

Answer 2

$|\overset{\rightarrow}{A}| = \sqrt{(2)^{2} + (4)^{2} + ( - 5)^{2}} = \sqrt{45}$

∴ $\cos\alpha = \frac{2}{\sqrt{45}},\cos\beta = \frac{4}{\sqrt{45}},\cos\gamma = \frac{- 5}{\sqrt{45}}$