A) \[0,\,\frac{1}{\sqrt{5}}\,,\,\frac{-2}{\sqrt{5}}\]
B) \[0,\,\frac{1}{\sqrt{5}}\,,\,\frac{1}{\sqrt{5}}\]
C) 0, 0, \[\frac{1}{\sqrt{5}}\]
D) None of these
Correct Answer: A
Solution :
| [a] \[(\vec{A}-\vec{B})=\sqrt{1+4}=\sqrt{5}\] |
| \[(\vec{A}-\vec{B})=\,2\hat{i}\,\,+3\hat{j}\,\,+\,\hat{k}\,-2\hat{i}-2\hat{j}-3\hat{k}\] |
| \[=\hat{j}-2\hat{k}\] |
| \[|\vec{A}-\vec{B}|=\sqrt{1+4}=\,\sqrt{5}\] |
| Direction cosine \[=\,\frac{0}{\sqrt{5}},\,\frac{1}{\sqrt{5}},\,-\frac{2}{\sqrt{5}}\] |
| i.e., \[=\,0,\,\frac{1}{\sqrt{5}},\,-\frac{2}{\sqrt{5}}\]. |
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