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CUET · MATHS · PYQ PAPER 2023

The angle between the line \(\frac{x+1}{2}=\frac{y}{3}=\frac{z-3}{6}\) and the plane \(10 x+2 y-11 z=3\) is :

  1. A \(\sin ^{-1}\left(-\frac{8}{21}\right)\)
  2. B \(\sin ^{-1}\left(-\frac{21}{8}\right)\)
  3. C \(\sin ^{-1}\left(\frac{21}{8}\right)\)
  4. D \(\sin ^{-1}\left(\frac{8}{21}\right)\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(\sin ^{-1}\left(\frac{8}{21}\right)\)

Step-by-step Solution

Detailed explanation

\(\vec{b} = \langle 2, 3, 6 \rangle\) \(|\vec{b}| = \sqrt{2^2 + 3^2 + 6^2} = 7\) \(\vec{n} = \langle 10, 2, -11 \rangle\) \(|\vec{n}| = \sqrt{10^2 + 2^2 + (-11)^2} = 15\) \(\vec{b} \cdot \vec{n} = (2)(10) + (3)(2) + (6)(-11) = 20 + 6 - 66 = -40\)…