TS EAMCET · Maths · Three Dimensional Geometry
If the direction ratios \(a, b, c\) of a line \(L\) satisfy the relations \(a b+b c+c a=0\) and \(6 a b+9 b c+8 c a=0\), then the direction cosines of the line \(L\) are
- A \(\frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}\)
- B \(\frac{2}{\sqrt{7}}, \frac{1}{\sqrt{7}}, \frac{-2}{\sqrt{7}}\)
- C \(\frac{-1}{\sqrt{6}}, \frac{\sqrt{3}}{\sqrt{6}}, \frac{\sqrt{2}}{\sqrt{6}}\)
- D \(\frac{-3}{7}, \frac{2}{7}, \frac{-6}{7}\)
Answer & Solution
Correct Answer
(D) \(\frac{-3}{7}, \frac{2}{7}, \frac{-6}{7}\)
Step-by-step Solution
Detailed explanation
Given relations \(a b+b c+c a=0\) and \(\quad 6 a b+9 b c+8 c a=0\) \(\therefore \quad 3 b c+2 a c=0 \Rightarrow 3 b+2 a=0\) and \(\quad-2 a b+b c=0 \Rightarrow 2 a-c=0\) \(\therefore \quad 2 a=-3 b=c \Rightarrow \frac{a}{-3}=\frac{b}{2}=\frac{c}{-6}\) or…
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