CUET · MATHS · PYQ PAPER 2025
Cosine of the acute angle between the lines \(\frac{x-3}{2}=\frac{y-2}{1}=\frac{x-5}{2}\) and \(\frac{x-1}{6}=\frac{y-3}{-3}=\frac{z+6}{2}\) is
- A \(\frac{11}{21}\)
- B \(\frac{13}{21}\)
- C \(\frac{10}{21}\)
- D \(\frac{8}{21}\)
Answer & Solution
Correct Answer
(B) \(\frac{13}{21}\)
Step-by-step Solution
Detailed explanation
Direction vectors are \(\vec{d_1} = \langle 2, 1, 2 \rangle\) and \(\vec{d_2} = \langle 6, -3, 2 \rangle\). \(\cos\theta = \frac{|\vec{d_1} \cdot \vec{d_2}|}{||\vec{d_1}|| ||\vec{d_2}||}\) \(\vec{d_1} \cdot \vec{d_2} = (2)(6) + (1)(-3) + (2)(2) = 12 - 3 + 4 = 13\)…
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