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Mathematics : Three Dimensional Geometry

Short Answer Type

211. Find the equation of the plane through the points (0, – 1, 0), (2, 1, –1) and (1,1,1).

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212. Find the equation of the plane passing through the points (0. – 1, 0), (1, 1, 1) and (3, 3,0).

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Long Answer Type

213. Find the equation of the plane through the three points (1, 1, 1), (1, – 1, 1) and (–7, – 3,–5).

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Short Answer Type

214.

Find the vector equation of the plane passing through the point A(2, 2, –1), B(3, 4, 2) and C (7, 0, 6). Also find the cartesian equation of the plane.

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215. Find the vector equations of the plane passing through the points R(2, 5, –3), S(– 2, – 3, 5) and T(5, 3, – 3).

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216. Find the equations of the planes that passes through three points:
(1, 1,–1), (6, 4, –5),(–4, –2, 3)

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217. Find the equations of the planes that passes through three points:
(1, 1, 0), (1, 2, 1), (–2, 2, –1)

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Long Answer Type

218. If from a point P (a, b, c) perpendiculars PA and PB are drawn to yz and zx-planes, then find the vector equation of the plane OAB.

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219. Find the equation of plane through the points (2, 2, 1), (9, 3, 6), and perpendicular to the plane 2x + 6y + 6z = 9.

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220. Find the equation of the plane through the points (2, 2, 1), (9, 3, 6) and perpendicular to the plane 2x + 6y + 6z – 1 = 0.

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