AP EAMCET · Maths · Three Dimensional Geometry
If \(l, m, n\) are the direction cosines of a line that is perpendicular to the lines having the direction ratios \(1,2,-1\) and \(1,-2,1\) then \((l+m+n)^2=\)
- A \(\frac{1}{20}\)
- B \(\frac{9}{5}\)
- C \(\frac{1}{5}\)
- D \(\frac{3}{20}\)
Answer & Solution
Correct Answer
(B) \(\frac{9}{5}\)
Step-by-step Solution
Detailed explanation
\((l, m, n)\) are direction cosine of a line that is perpendicular to the lines having direction ratios \((1,2,-1)\) and \((1,-2,1)\) \(\therefore l+2 m-n=0\) ...(i) \(l-2 m+n=0\) ...(ii) Adding (i) and (ii), \(2 l=0 \Rightarrow l=0\) From (i), \(2 m-n=0 \Rightarrow 2 m=n\)…
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