CUET · MATHS · PYQ PAPER 2025
If a line makes angle π/3 and π/4 with the positive directions of x-axis and y-axis respectively, then the acute angle made by the line with positive direction of z-axis is
- A π/2
- B π/4
- C π/3
- D 2π/3
Answer & Solution
Correct Answer
(C) π/3
Step-by-step Solution
Detailed explanation
\(\cos^2 \alpha + \cos^2 \beta + \cos^2 \gamma = 1\) \(\cos^2 (\pi/3) + \cos^2 (\pi/4) + \cos^2 \gamma = 1\) \((1/2)^2 + (1/\sqrt{2})^2 + \cos^2 \gamma = 1\) \(1/4 + 1/2 + \cos^2 \gamma = 1\) \(3/4 + \cos^2 \gamma = 1\) \(\cos^2 \gamma = 1/4\) \(\cos \gamma = 1/2\) (for acute…
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