Question

The direction cosines of the resultant of the vectors $\mathbf{r}.(\mathbf{i} - 2\mathbf{j} + 4\mathbf{k}) = 9$ $( - \mathbf{i} + \mathbf{j} + \mathbf{k}),$ $(\mathbf{i} - \mathbf{j} + \mathbf{k})$ and $(\mathbf{i} + \mathbf{j} - \mathbf{k}),$ are

• A. $\left( \frac{1}{\sqrt{2}},\frac{1}{\sqrt{3}},\frac{1}{\sqrt{6}} \right)$
• B. $\left( \frac{1}{\sqrt{6}},\frac{1}{\sqrt{6}},\frac{1}{\sqrt{6}} \right)$
• C. $\left( - \frac{1}{\sqrt{6}}, - \frac{1}{\sqrt{6}}, - \frac{1}{\sqrt{6}} \right)$
• D. $\left( \frac{1}{\sqrt{3}},\frac{1}{\sqrt{3}},\frac{1}{\sqrt{3}} \right)$

Answer 1

Answer: (D)

$\left( \frac{1}{\sqrt{3}},\frac{1}{\sqrt{3}},\frac{1}{\sqrt{3}} \right)$

Answer 2

Resultant vector $= 2\mathbf{i} + 2\mathbf{j} + 2\mathbf{k}.$

Direction cosines are $\left( \frac{1}{\sqrt{3}},\frac{1}{\sqrt{3}},\frac{1}{\sqrt{3}} \right).$