JEE Mains · Maths · STD 12 - 11. three dimension geometry
The plane passing through the line \(L: \ell x-y+3(1-\ell)\) \(z=1, x+2 y-z=2\) and perpendicular to the plane \(3 x+2 y+z=6\) is \(3 x-8 y+7 z=4\). If \(\theta\) is the acute angle between the line \(L\) and the \(y\)-axis, then \(415 \cos ^{2} \theta\) is equal to\(...\)
- A \(123\)
- B \(124\)
- C \(125\)
- D \(126\)
Answer & Solution
Correct Answer
(C) \(125\)
Step-by-step Solution
Detailed explanation
\(\vec{n}_{1}=\ell \hat{ i }-\hat{ j }+3(1-\ell) \hat{ k }\) \(\overrightarrow{ n }_{2}=\hat{ i }+2 \hat{ j }-\hat{ k }\) Direction ratio of line \(=\left|\begin{array}{ccc}\hat{ i } & \hat{ j } & \hat{ k } \\ \ell & -1 & 3(1-\ell) \\ 1 & 2 & -1\end{array}\right|\)…
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