AP EAMCET · Maths · Three Dimensional Geometry
If the line of intersection of the planes \(2 x+3 y+z=1\) and \(x+3 y+2 z=2\) makes an angle \(\alpha\) with the positive 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
\( \vec{n_1} = \langle 2, 3, 1 \rangle, \vec{n_2} = \langle 1, 3, 2 \rangle \) \( \vec{d} = \vec{n_1} \times \vec{n_2} = \begin{vmatrix} \mathbf{i} & \mathbf{j} & \mathbf{k} \\ 2 & 3 & 1 \\ 1 & 3 & 2 \end{vmatrix} = \langle 3, -3, 3 \rangle \)…
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