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in 3D Coordinate Geometry by (30.9k points)
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Find the coordinates of the point, where the line \(\frac{x-2}{3}=\frac{y+1}{4}=\frac{z-2}{2}\) intersects the plane x – y + z – 5 = 0. Also find the angle between the line and the plane.

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by (31.4k points)
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Best answer

Let the given line

intersect at point P (a, b, g) to the plane x - y + z - 5 = 0 ...(ii)

\(\because\) P \((\alpha, \beta, \gamma)\) lie on line (i)

Also, P \((\alpha, \beta, \gamma)\) lies on plane (ii)

Hence, co-ordinate of required point = (2, -1, 2)

Now, find angle between line (i) and plane (ii)

If θ be the required angle, then

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