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Solve the following.
Find the angle between the line and the plane .
Find the angle between the line $\frac{x+1}{2} = \frac{y}{3} = \frac{z-3}{6}$ and the plane $2x + 3y - 5z = 4$.
Answer
Answer
AIDirection ratios of the line: $(2, 3, 6)$; normal to the plane: $(2, 3, -5)$.
$\sin\theta = \frac{|2(2) + 3(3) + 6(-5)|}{\sqrt{4+9+36}\sqrt{4+9+25}} = \frac{17}{7\sqrt{38}}$.
Hence $\theta = \sin^{-1}\left(\frac{17}{7\sqrt{38}}\right)$ ($\approx 23.2^\circ$).
Final answer: $\sin^{-1}\left(\frac{17}{7\sqrt{38}}\right)$
From ISC 2018 Specimen Mathematics Paper 1, question 15(b).
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