If - is the angle between the line r - a - t b and the plane r- n - q is connected by the relation

The correct option is C sinθ = b. n|b| |n| If θ is the angle between the line r⃗ = a⃗ + tb⃗ and the plane r⃗.n⃗ = q, 90 #160; θ becom ...

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Standard XII

Mathematics

Angle between a Plane and a Line

If θ is the...

Question

If $θ$ is the angle between the line $\to r = \to a + t \to b$ and the plane $\to r . \to n = q$ is connected by the relation

cos θ = \frac{\to a . \to n}{q}

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cos θ = \frac{\to b . \to n}{| \to b | | \to n |}

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sin θ = \frac{\to a, \to b}{| \to n |}

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sin θ = \frac{\to b . \to n}{| \to b | | \to n |}

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Solution

The correct option is C $sin θ = \frac{\to b . \to n}{| \to b | | \to n |}$
If $θ$ is the angle between the line $\to r = \to a + t \to b$ and the plane $\to r . \to n = q, 90 - θ$ becomes the angle between the line and the normal $\to n$ to the plane.
Since the line is parallel to $\to b, cos (90 - θ) = \frac{\to b . \to n}{| \to b | | \to n |}$
$∴ sin θ = \frac{\to b . \to n}{| \to b | | \to n |}$

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If θ is the angle between the line →r=→a+t→b and the plane →r.→n=q is connected by the relation

If $θ$ is the angle between the line $\to r = \to a + t \to b$ and the plane $\to r . \to n = q$ is connected by the relation