Question types

Line and Plane question types

388 questions across 7 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.

388
Questions
7
Question groups
5
Question types
Sample Questions

Line and Plane questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

Q 1MCQ1 Mark
The foot of perpendicular drawn from the point (0,0,0) to the plane is (4, -2, -5) then the equation of the plane is
  • A
    4x + y + 5z = 14
  • 4x – 2y – 5z = 45
  • C
    x – 2y – 5z = 10
  • D
    4x + y + 6z = 11

Answer: B.

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Q 2MCQ1 Mark
If the line $\frac{x+1}{2}=\frac{y-m}{3}=\frac{z-4}{6}$ lies in the plane $3 x-14 y+6 z+49=0$, then the value of

m is:

  • 5
  • B
    3
  • C
    2
  • D
    -5

Answer: A.

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Q 3MCQ1 Mark
The equation of the plane in which the line $\frac{x-5}{4}=\frac{y-7}{4}=\frac{z+3}{-5}$ and $\frac{x-8}{7}=\frac{y-4}{1}=\frac{z+5}{3}$lie, is
  • 17x – 47y – 24z + 172 = 0
  • B
    17x + 47y – 24z + 172 = 0
  • C
    17x + 47y + 24z +172 = 0
  • D
    17x – 47y + 24z + 172 = 0

Answer: A.

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Q 4MCQ1 Mark
The equation of the plane passing through the points (1, -1, 1), (3, 2, 4) and parallel to Y-axis is :
  • A
    3x + 2z – 1 = 0
  • 3x – 2z = 1
  • C
    3x + 2z + 1 = 0
  • D
    3x + 2z = 2

Answer: B.

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Q 5MCQ1 Mark
The direction cosines of the normal to the plane 2x – y + 2z = 3 are
  • $\frac{2}{3}, \frac{-1}{3}+\frac{2}{3}$
  • B
    $\frac{-2}{3}, \frac{1}{3}, \frac{-2}{3}$
  • C
    $\frac{2}{3}, \frac{1}{3}, \frac{2}{3}$
  • D
    $\frac{2}{3}, \frac{-1}{3}, \frac{-2}{3}$

Answer: A.

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Find the vector equations of planes which pass through A(1, 2, 3), B (3, 2, 1) and make equal intercepts on the co-ordinates axes. Question is modified Find the cartesian equations of the planes which pass through A(1, 2, 3), B(3, 2, 1) and make equal intercepts on the coordinate axes.
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Reduce the equation $\bar{r} \cdot(3 \hat{i}-4 \hat{j}+12 \hat{k})=8$ to the normal form and hence find
(i) the length of the perpendicular from the origin to the plane
(ii) direction cosines of the normal.
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