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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 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:
  • ✓
    x - 4y + 2z + 4 = 0
  • B
    x + 4y + 2z + 4 = 0
  • C
    x - 4y + 2z - 4 = 0
  • D
    None of these

Answer: A.

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Q 2M.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:
  • A
    1
  • B
    2
  • ✓
    3
  • D
    None of these

Answer: C.

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Q 3M.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:
  • A
    $\frac{5}{3\sqrt{3}}$
  • ✓
    $\frac{10}{3\sqrt{3}}$
  • C
    $\frac{25}{3\sqrt{3}}$
  • D
    $\text{None of these}$

Answer: B.

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Q 5M.C.Q (1 Marks)1 Mark
The eqution of the plane $\vec{\text{r}}=\hat{\text{i}}-\hat{\text{j}}+\lambda(\hat{\text{i}}+\hat{\text{j}}+\hat{\text{k}})+\mu(\hat{\text{i}}-2\hat{\text{j}}+3\hat{\text{k}})$ in scalar product from is:
  • ✓
    $\vec{\text{r}}.(5\hat{\text{i}}-2\hat{\text{j}}-3\hat{\text{k}})=7$
  • B
    $\vec{\text{r}}.(5\hat{\text{i}}+2\hat{\text{j}}-3\hat{\text{k}})=7$
  • C
    $\vec{\text{r}}.(5\hat{\text{i}}-2\hat{\text{j}}+3\hat{\text{k}})=7$
  • D
    $\text{None of these}$

Answer: A.

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Q 92 Marks Questions2 Marks
Find the cartesian form of the equation of a plane whose vector equation is:
$\vec{\text{r}}\cdot\big(12\hat{\text{i}}-3\hat{\text{j}}+4\hat{\text{k}}\big)+5=0$
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Q 113 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 $\vec{\text{r}}\cdot(3\hat{\text{i}}+6\hat{\text{j}}-2\hat{\text{k}})=9$
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Q 165 Marks Questions5 Marks
Find the vector equation of the plane passing through the point (3, 4, 2) and (7, 0, 6) and perpendicular to the plane 2x - 5y - 15 = 0. Also, show that the plane thus obtaines contains the line
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Q 185 Marks Questions5 Marks
Find the equation of the plane through the line of intersection of the planes $\vec{\text{r}}\cdot(\hat{\text{i}}+3\hat{\text{j}})+6=0$ and $\vec{\text{r}}\cdot(3\hat{\text{i}}-\hat{\text{j}}-4\hat{\text{k}})=0,$ which is at a unit distance from the origin.
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Q 205 Marks Questions5 Marks
Find the equation of the plane passing through the line of intersection of the planes $2x - y = 0$ and $3z - y= 0$ and perpendicular to the plane $4x + 5y - 3z = 8$.
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