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MHT-CET Line and Plane — practice questions — page 2

Explore 35 free Line and Plane questions in MHT-CET Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Line and Plane questions and exercises with answers

Showing questions 31–35 of 35.

The plane through the origin and the intersection of x + y + z = 1 and 2x + 3y + 4z = 5 isRead the answer and worked solution →The plane through (1, 0, 0), (0, 1, 0) and (0, 0, 1) isRead the answer and worked solution →Normals to a given plane have direction ratios that areRead the answer and worked solution →A line in space is completely determined byRead the answer and worked solution →Lines with direction ratios 1, 2, 2 and 2, 1, k are perpendicular when k equalsRead the answer and worked solution →

Worked practice questions

The plane through the origin and the intersection of x + y + z = 1 and 2x + 3y + 4z = 5 is

  1. x + y + z = 0
  2. 3x + 2y + z = 0
  3. 2x + 3y + 4z = 0
  4. x + 2y + 3z = 0
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Correct answer: B. 3x + 2y + z = 0

The member (x+y+z-1) + λ(2x+3y+4z-5) passes through the origin when λ = -1/5, giving 3x + 2y + z = 0.

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The plane through (1, 0, 0), (0, 1, 0) and (0, 0, 1) is

  1. x + y + z = 0
  2. x + y - z = 1
  3. x + y + z = 1
  4. x - y + z = 1
Show answer and solution

Correct answer: C. x + y + z = 1

All three points satisfy x + y + z = 1, and three non-collinear points fix one plane.

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Normals to a given plane have direction ratios that are

  1. identical
  2. perpendicular
  3. proportional
  4. all negative
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Correct answer: C. proportional

Every normal is parallel to every other, so their direction ratios are proportional.

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More Mathematics topics

Permutations and CombinationsProbabilityApplication of DerivativesLinear ProgrammingDifferential EquationsVectorsDefinite IntegrationMatrices