251.Find the angle between the line and the plane 2x – y + z= 1.
The equation of line is Its direction ratios are 1, – 1, 1 The equation of plane is 2x –y + z = 1 ∴ direction ratios of the normal to the plane are 2, – 1, 1. Let θ be the angle between the line and plane.
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252.
Find the angle between the line and the plane 2x + y – 3z + 4 = 0.
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253.Find the angle between the lines and the plane 10x + 2y – 11z = 3.
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254.Find the angle between the line and the plane 3x + 4y + z + 5 = 0.
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255.
Find the angle between the line and the plane
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256.Find the distance between the parallel planes: 2x – 3y + z + 3 = 0 and 4x – 6y + 2z + 5 = 0
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257.Find the distance between parallel planes: 2x – y + 3z – 4 = 0 and 6x – 3y + 9z + 13 = 0.
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258.Find the distance between the planes and
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Long Answer Type
259.Find the length and coordinates of the foot of the perpendicular from the point (1, 1, 2) to the plane 2x – 2y + 4z + 5 = 0.
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260.Find the distance between the point P(6, 5, 9) and the plane determined by the points A(3, –1, 2), B(5, 2, 4) and C(– 1, – 1, 6).
Short Answer Type
Long Answer Type
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