Hello students, we are providing assertion reason questions for class 12. Assertion Reason questions are the new question format that is introduced in CBSE board. The resources for assertion reason questions are very less. So, to help students we have created chapterwise assertion reason questions for class 12 maths. In this article, you will find assertion reason questions for CBSE Class 12 Maths Chapter 11 Three Dimensional Geometry. It is a part of Assertion Reason Questions for CBSE Class 12 Maths Series.
| Chapter | Three Dimensional Geometry |
| Type of Questions | Assertion Reason Questions |
| Nature of Questions | Competency Based Questions |
| Board | CBSE |
| Class | 12 |
| Subject | Maths |
| Useful for | Class 12 Studying Students |
| Answers provided | Yes |
| Difficulty level | Mentioned |
| Important Link | Class 12 Maths Chapterwise Assertion Reason |
Assertion Reason Questions on Three Dimensional Geometry
Assertion Reason Questions
Directions: Each of the following questions consists of two statements: an Assertion (A) and a Reason (R). Answer them by selecting the correct option:
(a) Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct explanation of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).
(c) Assertion (A) is true, but Reason (R) is false.
(d) Assertion (A) is false, but Reason (R) is true.
Q1. Assertion (A): Two lines in 3D space are said to be skew lines if they are neither parallel nor intersecting.
Reason (R): Skew lines lie in the same plane.
Answer: (c) A is true, but R is false.
Difficulty Level: Moderate
Q2. Assertion (A): The direction cosines of a line are always real numbers.
Reason (R): They are defined using the cosine of angles made with coordinate axes.
Answer: (a) Both A and R are true, and R is the correct explanation of A.
Difficulty Level: Moderate
Q3. Assertion (A): The shortest distance between two skew lines can be found using the formula involving cross product of direction vectors.
Reason (R): Cross product gives a vector perpendicular to both lines.
Answer: (a) Both A and R are true, and R is the correct explanation of A.
Difficulty Level: Tough
Q4. Assertion (A): If the angle between two lines is 90°, then the dot product of their direction ratios is zero.
Reason (R): Cos(90°) = 0, and dot product involves cosine of the angle.
Answer: (a) Both A and R are true, and R is the correct explanation of A.
Difficulty Level: Moderate
Q5. Assertion (A): The angle between the line $\vec{r}=\vec{a}+\lambda \vec{b}$ and the plane $\vec{n} \cdot\left(\vec{r}-\vec{r}_0\right)=0$ is given by $\theta=$ $\cos ^{-1}\left(\frac{\vec{b} \cdot \vec{n}}{|\vec{b}||\vec{n}|}\right)$.
Reason $(R)$ : The angle between a line and a plane is the same as between the direction vector of the line and the normal to the plane.
Answer: (b) Both $A$ and $R$ are true, but $R$ is not the correct explanation of $A$.
Difficulty Level: Tough
Also check
- Probability Class 12 Assertion Reason Questions Maths Chapter 13
- Linear Programming Class 12 Assertion Reason Questions Maths Chapter 12
- Three Dimensional Geometry Class 12 Assertion Reason Questions Maths Chapter 11
- Vectors Class 12 Assertion Reason Questions Maths Chapter 10
- Differential Equations Class 12 Assertion Reason Questions Maths Chapter 9
- Applications of the Integrals Class 12 Assertion Reason Questions Maths Chapter 8
- Integrals Class 12 Assertion Reason Questions Maths Chapter 7
- Applications of Derivatives Class 12 Assertion Reason Questions Maths Chapter 6
- Continuity and Differentiability Class 12 Assertion Reason Questions Maths Chapter 5
- Determinants Class 12 Assertion Reason Questions Maths Chapter 4
- Matrices Class 12 Assertion Reason Questions Maths Chapter 3
- Inverse Trigonometric Functions Class 12 Assertion Reason Questions Maths Chapter 2
- Relations and Functions Class 12 Assertion Reason Questions Maths Chapter 1
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Topics from which assertion reason questions may be asked
- Direction Cosines and Ratios
- Line and Plane Equations
- Angle between Lines/Planes
3D geometry helps in solving spatial problems using vectors and coordinates.
Assertion reason questions from the above given topic may be asked.
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Frequently Asked Questions (FAQs) on Three Dimensional Geometry Assertion Reason Questions Class 12
Q1: What does the chapter ‘Three Dimensional Geometry’ cover?
A1: It builds key concepts related to three dimensional geometry and prepares you for logical reasoning-based questions.
Q2: What are assertion reason questions?
A2: These consist of two statements: an assertion and a reason. Students need to determine their correctness and relationship.
Q3: Why practice assertion reason questions in Three Dimensional Geometry?
A3: They strengthen core concepts and boost confidence in tackling tricky scenarios from three dimensional geometry.
Q4: Are assertion reason questions part of CBSE board exams?
A4: Yes, they are included under competency-based formats to test depth of understanding.
