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The plane Maths - The plane

Gujarat Board (GSEB) - STD 12 Science - Maths (GSEB - English Medium). 235 questions in this chapter.

Question types

The plane question types

235 questions across 4 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.

235
Questions
4
Question groups
5
Question types
Sample Questions

The plane questions

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

Q 1M.C.Q (1 Marks)1 Mark
The distance between the planes 2x + 2y - z +2 = 0 and 4x + 4y - 2z + 5 = 0 is:

  1. $\frac{1}{2}$

  2. $\frac{1}{4}$

  3. $\frac{1}{6}$

  4. $\text{None of these}$

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Q 2M.C.Q (1 Marks)1 Mark
The equation of the plane parallel to the lines x - 1 = 2y - 5 = 2z and 3x = 4y - 11 = 3z -4 and passing through the point (2, 3, 3) is:
  1. x - 4y + 2z + 4 = 0
  2. x + 4y + 2z + 4 = 0
  3. x - 4y + 2z - 4 = 0
  4. None of these
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Q 3M.C.Q (1 Marks)1 Mark
The distance between the point (3, 4, 5) and the point where the line $\frac{\text{x}-3}{\text{1}}=\frac{\text{y}-4}{\text{2}}=\frac{\text{z}-5}{\text{2}}$ meets the plane x + y + z = 17 is:
  1. 1
  2. 2
  3. 3
  4. None of these
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Q 4M.C.Q (1 Marks)1 Mark
The distance of the line $\vec{\text{r}}=2\hat{\text{i}}-2\hat{\text{j}}+3\hat{\text{k}}+\lambda(\hat{\text{i}}-\hat{\text{j}}+4\hat{\text{k}})$ from the plane $\vec{\text{r}}.(\hat{\text{i}}+5\hat{\text{j}}+\hat{\text{k}})=5$ is:

  1. $\frac{5}{3\sqrt{3}}$

  2. $\frac{10}{3\sqrt{3}}$

  3. $\frac{25}{3\sqrt{3}}$

  4. $\text{None of these}$

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Q 5M.C.Q (1 Marks)1 Mark
The plane $2\text{x}-(1-\lambda)\text{y}+3\lambda\text{z}=0$ passes through the intersection of the planes:
  1. 2x - y = 0 and y- 3z = 0
  2. 2x + 3z = 0 and y = 0
  3. 2x - y + 3z = 0 and y - 3z = 0
  4. None of these
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Q 62 Marks2 Marks
Find the vector equation of a plane which is at a distance of 3 units from the origin and has $\hat{\text{k}}$ as the unit vector normal to it.
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Q 113 Marks3 Marks
A plane meets the coordinate axes at A, B and C, respectively, such that the centriod of triangle ABC is (1, -2, 3). Find the equation of the plane.
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Q 123 Marks3 Marks
Find the vector and cartesian equations of a plane passing through the point (1, -1, 1) and normal to the line joining the points (1, 2, 5) and (-1, 3, 1)
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Q 133 Marks3 Marks
Reduce the equation of the following planes to intercept from and find the intercepts on the coordinate axes:
4x + 3y - 6z - 12 = 0
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Q 143 Marks3 Marks
Find the distance of the point P(-1, -5, -10) from the point of intersection of the line joining the points A(2, -1, 2) and B(5, 3, 4) with the plane x - y + z = 5.
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Q 174 Marks4 Marks
If the axes are rectangular and p is the point (2, 3, -1), find the equation of the plane throught p at right angles to OP.
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Q 184 Marks4 Marks
Find the length and the foot ofo perpendicular from the point $\Big(1,\frac{3}{2},2\Big)$ to the plane 2x - 2y + 4z + 5 = 0
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Q 194 Marks4 Marks
Find the shortest distance between the lines $\frac{\text{x}-1}{2}=\frac{\text{y}-3}{4}=\frac{\text{z}+2}{1}$ and 3x - y - 2z + 4 = 0 = 2x + y + z + 1.
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Q 204 Marks4 Marks
Find the vector and cartesian equations of the line passing through (1, 2, 3) and parallel to the planes $\vec{\text{r}}\cdot(\hat{\text{i}}-\hat{\text{j}}+2\hat{\text{k}})=5$ and $\vec{\text{r}}\cdot(3\hat{\text{i}}+\hat{\text{j}}+2\hat{\text{k}})=6$
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