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The plane Maths - The plane

Maharashtra Board - STD 12 - Maths (MSBSHSE - Semi 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 1MCQ1 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 2MCQ1 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 3MCQ1 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 4MCQ1 Mark
The image of the point $(1, 3, 4)$ in the plane $2x - y + z + 3 = 0$ is:
  • A
    $(3, 5, 2)$
  • ✓
    $(-3, 5, 2)$
  • C
    $(3, 5, -2)$
  • D
    $(3, -5, 2)$

Answer: B.

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Q 5MCQ1 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 18Solve the Following Question.(5 Marks)5 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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