TS EAMCET · Maths · Three Dimensional Geometry
A line \(L\) is parallel to both the planes \(2 x+3 y+z=1\) and \(x+3 y+2 z=2\). If line \(L\) makes an angle \(\alpha\) with the positive direction of X-axis, then \(\cos \alpha=\)
- A \(\frac{1}{\sqrt{3}}\)
- B \(\frac{1}{\sqrt{2}}\)
- C \(\frac{1}{2}\)
- D \(\frac{\sqrt{3}}{2}\)
Answer & Solution
Correct Answer
(A) \(\frac{1}{\sqrt{3}}\)
Step-by-step Solution
Detailed explanation
Line parallel to both planes will be perpendicular to Angle with \(X\) axis \(=\alpha\) \[ \begin{aligned} & \therefore \quad \cos \alpha=\frac{3}{\sqrt{3^2+(-3)^2+3^2}}=\frac{3}{3 \sqrt{3}} \\ & \therefore \quad \cos \alpha=\frac{1}{\sqrt{3}} . \end{aligned} \]
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