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CUET · MATHS · PYQ PAPER 2023

The angle between the line \(\frac{x+2}{3}=\frac{y-3}{2}=\frac{z+5}{6}\) and the plane 2x + 10y - 11z = 5 is:

  1. A \(\cos ^{-1}\left(\frac{8}{21}\right)\)
  2. B \(\sin ^{-1}\left(\frac{8}{21}\right)\)
  3. C \(\cos ^{-1}\left(\frac{21}{82}\right)\)
  4. D \(\sin ^{-1}\left(\frac{21}{82}\right)\)
Verified Solution

Answer & Solution

Correct Answer

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

Step-by-step Solution

Detailed explanation

\(\vec{b} = \langle 3, 2, 6 \rangle\) \(\vec{n} = \langle 2, 10, -11 \rangle\) \(\sin \theta = \frac{|\vec{b} \cdot \vec{n}|}{||\vec{b}|| \cdot ||\vec{n}||}\) \(\sin \theta = \frac{|(3)(2) + (2)(10) + (6)(-11)|}{\sqrt{3^2+2^2+6^2} \cdot \sqrt{2^2+10^2+(-11)^2}}\)…