Q.1 (iii) If α, β, γ are direction angles of a line and α = 60^° , β = 45^° , then γ = _____. A. 30° or 90° B. 45° or 60° C. 90° or 130° D. 60° or 120°

Answer: D. 60° or 120° Answer: (d) 60° or 120° cos²α + cos²β + cos²γ = 1 ⇒ 1/4 + 1/2 + cos²γ = 1 ⇒ cos²γ = 1/4 . So cosγ = ±1/2 , giving γ = 60^° or 120^° .

If \(\alpha, \beta, \gamma\) are direction angles of a line and \(\alpha = 60^\circ\), \(\beta = 45^\circ\), then \(\gamma =\) _____.

Q.1 (iii) If \(\alpha, \beta, \gamma\) are direction angles of a line and \(\alpha = 60^\circ\), \(\beta = 45^\circ\), then \(\gamma =\) _____.

A. 30° or 90°

B. 45° or 60°

C. 90° or 130°

D. 60° or 120°

Doubtly Asked 29 Oct 2026 Board exam · March 2024 hsc 12th Save WhatsApp Report

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Answer: D. 60° or 120°

Answer: (d) 60° or 120°

\(\cos^2\alpha + \cos^2\beta + \cos^2\gamma = 1 \Rightarrow \frac{1}{4} + \frac{1}{2} + \cos^2\gamma = 1 \Rightarrow \cos^2\gamma = \frac{1}{4}\).

So \(\cos\gamma = \pm\frac{1}{2}\), giving \(\gamma = 60^\circ\) or \(120^\circ\).

Doubtly AI · 29 Oct 2026 AI-generated · not yet verified Report

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If \(\alpha, \beta, \gamma\) are direction angles of a line and \(\alpha = 60^\circ\), \(\beta = 45^\circ\), then \(\gamma =\) _____.

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