TS EAMCET · Maths · Three Dimensional Geometry
The direction cosines of two lines are connected by the relation \(l-m+n=0\) and \(2 l m-3 m n+n l=0\). If \(\theta\) is the angle between these two lines, then \(\cos \theta=\)
- A \(\frac{1}{4}\)
- B \(\frac{1}{\sqrt{19}}\)
- C \(\frac{1}{3}\)
- D \(\frac{1}{3 \sqrt{2}}\)
Answer & Solution
Correct Answer
(B) \(\frac{1}{\sqrt{19}}\)
Step-by-step Solution
Detailed explanation
Given : \(l-m+n=0\) \(\Rightarrow m=l+n\) \(\qquad ....\mathrm{(i)}\) Substituting in \(2 l m-3 mn+n l=0\) \(\begin{aligned} & \Rightarrow 2 l^2-3 n^2=0 \qquad ....\mathrm{(ii)} \\ & \Rightarrow l=\sqrt{\frac{3}{2}} n, l=-\sqrt{\frac{3}{2}} n \end{aligned}\) From (i),…
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