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CUET · MATHS · PYQ PAPER 2025

Acute angle between the lines \(\frac{x}{3}=\frac{y}{4}=\frac{z}{5}\) and \(\frac{x-1}{4}=\frac{y+1}{-3}=\frac{z+10}{5}\) is :

  1. A \(\frac{\pi}{2}\)
  2. B \(\frac{\pi}{3}\)
  3. C \(\frac{\pi}{6}\)
  4. D \(\frac{\pi}{4}\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(\frac{\pi}{3}\)

Step-by-step Solution

Detailed explanation

\(\vec{d_1} = (3, 4, 5)\) \(\vec{d_2} = (4, -3, 5)\) \(\cos \theta = \frac{|\vec{d_1} \cdot \vec{d_2}|}{||\vec{d_1}|| \cdot ||\vec{d_2}||}\) \(\cos \theta = \frac{|(3)(4) + (4)(-3) + (5)(5)|}{\sqrt{3^2 + 4^2 + 5^2} \cdot \sqrt{4^2 + (-3)^2 + 5^2}}\)…