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MHT-CET Line and Plane — practice questions

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 1–30 of 35.

In the equation r = a + λb of a line, the scalar λ is calledRead the answer and worked solution →The non-parametric vector form of the line through A(a) parallel to b isRead the answer and worked solution →The line through (2, -1, 3) with direction ratios 1, 2, -2 isRead the answer and worked solution →For x = 1 + 2λ, y = 3 - λ, z = 4λ, the point at λ = 2 isRead the answer and worked solution →A line in space in Cartesian form is described byRead the answer and worked solution →The line through points with position vectors i + j and 3i + 5j + 2k isRead the answer and worked solution →Which point lies on the line (x - 1)/1 = (y - 1)/2 = (z - 1)/3?Read the answer and worked solution →Skew lines are lines in space thatRead the answer and worked solution →Two skew lines in space are alwaysRead the answer and worked solution →The shortest distance between two lines that intersect at a point isRead the answer and worked solution →The shortest distance between the x-axis and the line through (0, 0, 3) parallel to the y-axis isRead the answer and worked solution →A line perpendicular to a plane is calledRead the answer and worked solution →The direction ratios of a normal to the XY plane areRead the answer and worked solution →The plane through A(a) perpendicular to the vector n has equationRead the answer and worked solution →The plane through (1, 2, 3) with normal vector 2i - j + 4k isRead the answer and worked solution →In the plane ax + by + cz + d = 0, the numbers a, b, c areRead the answer and worked solution →The plane at distance p from the origin with unit normal n has equationRead the answer and worked solution →If l, m, n are the direction cosines of the normal, the normal form of the plane isRead the answer and worked solution →A plane is 7 units from the origin with normal cosines 2/7, 3/7, 6/7. The foot of the perpendicular isRead the answer and worked solution →Before finding the distance of a point from a plane by the vector method, the plane must be inRead the answer and worked solution →Planes 2x + 3y + kz = 5 and x - 2y + 4z = 1 are perpendicular when k equalsRead the answer and worked solution →The angle between two planes that are not perpendicular is defined as the angle between their normals that isRead the answer and worked solution →A line-plane angle is the complement of the acute angle between the line andRead the answer and worked solution →The angle between a line and a plane can never beRead the answer and worked solution →The line r = a + λb is perpendicular to the plane r · n = d if and only ifRead the answer and worked solution →The line with direction ratios 2, 3, -1 is parallel to the plane kx + y + 5z = 7 when k isRead the answer and worked solution →Two parallel lines are alwaysRead the answer and worked solution →If the distance between two non-parallel lines is zero, then the lines areRead the answer and worked solution →The plane containing two coplanar lines r = a1 + λb1 and r = a2 + μb2 has a normal alongRead the answer and worked solution →Which plane passes through the line of intersection of r · n1 = d1 and r · n2 = d2?Read the answer and worked solution →

Worked practice questions

In the equation r = a + λb of a line, the scalar λ is called

  1. a direction cosine
  2. a scalar parameter
  3. a position vector
  4. a unit normal
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Correct answer: B. a scalar parameter

Each real value of λ gives exactly one point of the line, which makes λ the parameter of the line.

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The non-parametric vector form of the line through A(a) parallel to b is

  1. (r - a) · b = 0
  2. (r + a) × b = 0
  3. (r - a) × b = 0
  4. r × a = b
Show answer and solution

Correct answer: C. (r - a) × b = 0

The vector AP = r - a is parallel to b, so its cross product with b vanishes.

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The line through (2, -1, 3) with direction ratios 1, 2, -2 is

  1. (x + 2)/1 = (y - 1)/2 = (z + 3)/(-2)
  2. (x - 2)/1 = (y + 1)/2 = (z - 3)/(-2)
  3. (x - 2)/2 = (y + 1)/(-1) = (z - 3)/3
  4. (x - 1)/2 = (y - 2)/(-1) = (z + 2)/3
Show answer and solution

Correct answer: B. (x - 2)/1 = (y + 1)/2 = (z - 3)/(-2)

Subtract the point coordinates in each numerator: x - 2, y + 1 and z - 3, over the ratios 1, 2, -2.

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More Mathematics topics

Permutations and CombinationsProbabilityApplication of DerivativesLinear ProgrammingDifferential EquationsVectorsDefinite IntegrationMatrices