A) \[\sqrt{\frac{5}{3}}\]
B) \[\sqrt{\frac{3}{5}}\]
C) \[-\frac{3}{5}\]
D) \[-\frac{5}{3}\]
Correct Answer: A
Solution :
Direction Ratio of line are\[2,1,-2\] | |
Normal vector of plane is \[\hat{i}-2\hat{j}-k\hat{k}\] | |
\[\sin \alpha =\frac{\left( 2\hat{i}+\hat{j}-\hat{k} \right).\left( \hat{i}-2\hat{j}-k\hat{k} \right)}{3\sqrt{1+4+{{k}^{2}}}}\] | |
\[\sin \alpha =\frac{2k}{3\sqrt{{{k}^{2}}+5}}\] | ? (1) |
\[\cos \alpha =\frac{2\sqrt{2}}{3}\] (Given) | ? (2) |
Using, \[{{\sin }^{2}}\alpha +{{\cos }^{2}}\alpha =1\]\[\Rightarrow \] \[{{k}^{2}}=\frac{5}{3}\]\[\Rightarrow \] \[k=\sqrt{\frac{5}{3}}.\] |
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