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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).

91 Views

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)

The given points are (1,1, 0), (1, 2,1), (–2, 2, –1).
These points are not collinear.
The equation of plane passing through these points is
$open vertical bar table row cell straight x minus 1 end cell cell straight y minus 1 end cell cell straight z minus 0 end cell row cell 1 minus 1 end cell cell 2 minus 1 end cell cell 1 minus 0 end cell row cell negative 2 minus 1 end cell cell 2 minus 1 end cell cell negative 1 minus 0 end cell end table close vertical bar space equals 0$

or $open vertical bar table row cell straight x minus 1 end cell cell straight y minus 1 end cell straight z row 0 1 1 row cell negative 3 end cell 1 cell negative 1 end cell end table close vertical bar space equals space 0$

$or space space open parentheses straight x minus 1 close parentheses space space open vertical bar table row 1 1 row 1 cell negative 1 end cell end table close vertical bar space minus space left parenthesis straight y minus 1 right parenthesis space open vertical bar table row 0 1 row cell negative 3 end cell cell negative 1 end cell end table close vertical bar space plus space straight z space open vertical bar table row 0 1 row cell negative 3 end cell 1 end table close vertical bar space equals space 0 or space space left parenthesis straight x minus 1 right parenthesis thin space left parenthesis negative 1 minus 1 right parenthesis space minus space left parenthesis straight y minus 1 right parenthesis space left parenthesis 0 plus 3 right parenthesis space plus space straight z space left parenthesis 0 plus 3 right parenthesis space equals space 0 or space space minus 2 straight x plus 2 minus 3 straight y plus 3 plus space 3 straight z space equals space 0 space space space space space or space space space 2 straight x plus 3 straight y minus 3 straight z space equals space 5$

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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.

100 Views

Previous Year Papers

Test Series

Test Yourself

Short Answer Type

Long Answer Type

Short Answer Type

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

Long Answer Type

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