Download App

The plane MATHS - The plane

Rajasthan Board (RBSE) - STD 12 Science - MATHS (Rajasthan - 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 :
  • A
    $\frac{1}{2}$
  • B
    $\frac{1}{4}$
  • ✓
    $\frac{1}{6}$
  • D
    None of these

Answer: C.

View full solution →
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
View full solution →
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
View full solution →
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. $\text{None of these}$
View full solution →
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
View full solution →
Q 102 Marks Questions2 Marks
Find the cartesian form of the equation of a plane whose vector equation is:
$\vec{\text{r}}\cdot\big(12\hat{\text{i}}-3\hat{\text{j}}+4\hat{\text{k}}\big)+5=0$ 
View full solution →
Q 113 Marks Question3 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.
View full solution →
Q 133 Marks Question3 Marks
Find the angle between the given planes.
$\vec{\text{r}}\cdot(2\hat{\text{i}}-\hat{\text{j}}+2\hat{\text{k}})=6$ and $\vec{\text{r}}\cdot(3\hat{\text{i}}+6\hat{\text{j}}-2\hat{\text{k}})=9$
View full solution →
Q 165 Marks Questions5 Marks
If the lines $\frac{\text{x}-1}{-3}=\frac{\text{y}-2}{-2\text{k}}=\frac{\text{z}-3}{2}$ and $\frac{\text{x}-1}{\text{k}}=\frac{\text{y}-2}{1}=\frac{\text{z}-3}{5}$ are perpendicular, find the value of $k$ and, hence find the equation of the plane containing these lines.
View full solution →
Browse all question groups ↑

Generate a The plane paper free

Pick question groups from the list above, set marks and difficulty, and export a branded PDF with step-by-step answer keys. First 3 chapters free — no signup.

Download App
Generate Paper FreeAll MATHS chapters