Q.1 (iii) The angle between the lines bar r=(hat i+2hat j-3hat k)+λ(3hat i+2hat j+6hat k) and bar r=(5hat i-2hat j+7hat k)+μ(hat i+2hat j+2hat k) is ____. A. cos⁻¹(17/21) B. cos⁻¹(20/21) C. cos⁻¹(18/21) D. cos⁻¹(19/21)

Answer: D. cos⁻¹(19/21) Answer: (d) cos⁻¹(19/21) Direction vectors: bar b₁=3hat i+2hat j+6hat k , |bar b₁|=√(9+4+36)=7 ; bar b₂=hat i+2hat j+2hat k , |bar b₂|=3 . cosθ=|bar b₁·bar b₂|/|bar b₁||bar b₂|=3+4+12/7×3=19/21 , so θ=cos⁻¹(19/21) .

Chapter: Line and Plane· Mathematics & Statistics Part 1

The angle between the lines \(\bar r=(\hat i+2\hat j-3\hat k)+\lambda(3\hat i+2\hat j+6\hat k)\) and \(\bar r=(5\hat i-2\hat j+7\hat k)+\mu(\hat i+2\hat j+2\hat k)\) is ____.

Q.1 (iii) The angle between the lines \(\bar r=(\hat i+2\hat j-3\hat k)+\lambda(3\hat i+2\hat j+6\hat k)\) and \(\bar r=(5\hat i-2\hat j+7\hat k)+\mu(\hat i+2\hat j+2\hat k)\) is ____.

A. \(\cos^{-1}\left(\dfrac{17}{21}\right)\)

B. \(\cos^{-1}\left(\dfrac{20}{21}\right)\)

C. \(\cos^{-1}\left(\dfrac{18}{21}\right)\)

D. \(\cos^{-1}\left(\dfrac{19}{21}\right)\)

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

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Answer: D. \(\cos^{-1}\left(\dfrac{19}{21}\right)\)

Answer: (d) \(\cos^{-1}\left(\dfrac{19}{21}\right)\)

Direction vectors: \(\bar b_1=3\hat i+2\hat j+6\hat k\), \(|\bar b_1|=\sqrt{9+4+36}=7\); \(\bar b_2=\hat i+2\hat j+2\hat k\), \(|\bar b_2|=3\).

\(\cos\theta=\dfrac{|\bar b_1\cdot\bar b_2|}{|\bar b_1||\bar b_2|}=\dfrac{3+4+12}{7\times3}=\dfrac{19}{21}\), so \(\theta=\cos^{-1}\left(\dfrac{19}{21}\right)\).

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

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The angle between the lines \(\bar r=(\hat i+2\hat j-3\hat k)+\lambda(3\hat i+2\hat j+6\hat k)\) and \(\bar r=(5\hat i-2\hat j+7\hat k)+\mu(\hat i+2\hat j+2\hat k)\) is ____.

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