A) \[\frac{\hat{i}\,+\,\hat{j}\,+\,\hat{k}}{\sqrt{2}}\]
B) \[\frac{\hat{i}\,+\,\hat{j}\,+\,\hat{k}}{\sqrt{3b}}\]
C) \[\hat{i}\,+\,\hat{j}\,+\,\hat{k}\]
D) \[\frac{\hat{i}\,+\,\hat{j}\,+\,\hat{k}}{\sqrt{3}}\]
Correct Answer: D
Solution :
| [d] Diagonal vector \[\vec{A}\,=b\hat{i}+b\hat{j}+b\hat{k}\] |
| or \[A=\sqrt{{{b}^{2}}+{{b}^{2}}+{{b}^{2}}}\,=\,\sqrt{3}\,b\] |
| \[\therefore \] \[\hat{A}\,\,=\frac{{\vec{A}}}{A}=\,\frac{\hat{i}+\hat{j}+\,\hat{k}}{\sqrt{3}}\] |
| \[\therefore \] \[\hat{A}\,=\frac{{\vec{A}}}{A}=\,\frac{\hat{i}+\hat{j}+\hat{k}}{\sqrt{3}}\] |
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