A) \[\frac{3}{\sqrt{56}},\frac{-4}{\sqrt{56}},\frac{6}{\sqrt{56}}\]
B) \[\frac{3}{\sqrt{29}},\frac{-4}{\sqrt{29}},\frac{6}{\sqrt{29}}\]
C) \[\frac{3}{\sqrt{61}},\frac{-4}{\sqrt{61}},\frac{6}{\sqrt{61}}\]
D) \[4,-3,2\]
E) \[\frac{4}{\sqrt{29}},\frac{-3}{\sqrt{29}},\frac{2}{\sqrt{29}}\]
Correct Answer: C
Solution :
\[4x-4=1-3y=2z-1\] \[\Rightarrow \] \[\frac{x-1}{\frac{1}{4}}=\frac{y-\frac{1}{3}}{-\frac{1}{3}}=\frac{z-\frac{1}{2}}{\frac{1}{2}}\] \[\therefore \]Direction cosines are \[\frac{\frac{1}{4}}{\sqrt{\frac{1}{16}+\frac{1}{9}+\frac{1}{4}}},\frac{-\frac{1}{3}}{\sqrt{\frac{1}{16}+\frac{1}{9}+\frac{1}{4}}},\frac{\frac{1}{2}}{\sqrt{\frac{1}{16}+\frac{1}{9}+\frac{1}{4}}}\] \[=\frac{3}{\sqrt{61}},\frac{-4}{\sqrt{61}},\frac{6}{\sqrt{61}}\]
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