JEE Mains · Maths · STD 12 - 11. three dimension geometry
If the line of intersection of the planes \(a x+b y=3\) and \(ax + by + cz =0, a >0\) makes an angle \(30^{\circ}\) with the plane \(y - z +2=0\), then the direction cosines of the line are.
- A \(\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}, 0\)
- B \(\frac{1}{\sqrt{2}}, \frac{-1}{\sqrt{2}}, 0\)
- C \(\frac{1}{\sqrt{5}},-\frac{2}{\sqrt{5}}, 0\)
- D \(A\) or \(B\) or both
Answer & Solution
Correct Answer
(D) \(A\) or \(B\) or both
Step-by-step Solution
Detailed explanation
\(\begin{array}{l}\overrightarrow{ n }=\left|\begin{array}{ccc}\hat{ i } & \hat{ j } &\hat{ k } \\a & b & 0 \\a & b & c\end{array}\right| \\= bc \hat{ i }- ac \hat {j }\end{array}\) Direction ratios of line are \(b ,- a , 0\) Direction ratios of normal of the plane…
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