The direction cosines of the resultant of the vectors \[(\mathbf{i}+\mathbf{j}+\mathbf{k}),\] \[(-\mathbf{i}+\mathbf{j}+\mathbf{k}),\] \[(\mathbf{i}-\mathbf{j}+\mathbf{k})\] and \[(\mathbf{i}+\mathbf{j}-\mathbf{k}),\] are

\[\left( \frac{1}{\sqrt{2}},\,\,\frac{1}{\sqrt{3}},\,\,\frac{1}{\sqrt{6}} \right)\]

\[\left( \frac{1}{\sqrt{6}},\,\,\frac{1}{\sqrt{6}},\,\,\frac{1}{\sqrt{6}} \right)\]

\[\left( -\frac{1}{\sqrt{6}},\,\,-\frac{1}{\sqrt{6}},\,-\,\frac{1}{\sqrt{6}} \right)\]

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

The direction cosines of the resultant of the vectors \[(\mathbf{i}+\m

1.	The direction cosines of the resultant of the vectors \[(\mathbf{i}+\mathbf{j}+\mathbf{k}),\] \[(-\mathbf{i}+\mathbf{j}+\mathbf{k}),\] \[(\mathbf{i}-\mathbf{j}+\mathbf{k})\] 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» E.

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The direction cosines of the resultant of the vectors \[(\mathbf{i}+\mathbf{j}+\mathbf{k}),\] \[(-\mathbf{i}+\mathbf{j}+\mathbf{k}),\] \[(\mathbf{i}-\mathbf{j}+\mathbf{k})\] and \[(\mathbf{i}+\mathbf{j}-\mathbf{k}),\] are

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