Free PDF Download: Vector Algebra Class 12 Maths Chapter Guide for 2025-26
FAQs on Download NCERT Class 12 Maths Vector Algebra Book PDF (2025-26)
1. Which topics from Vector Algebra hold the most marks weightage for the CBSE Class 12 Maths board exam 2025-26?
For the CBSE Class 12 Maths exam, the most important and high-weightage topics in Vector Algebra typically include:
- Product of Vectors: This is a crucial area. Expect questions on the scalar (dot) product and vector (cross) product, including their properties and geometrical interpretations (like finding projection, area of a parallelogram, or area of a triangle).
- Scalar Triple Product: Questions asking to determine the volume of a parallelepiped or to check the coplanarity of three vectors are frequently asked and are often high-scoring.
- Section Formula: Problems based on internal and external division of a line segment are a recurring type of important question.
2. What are some expected 3-mark important questions from the scalar (dot) product of vectors?
In the 3-mark category for the board exam, you can expect questions from the dot product that test your understanding of its properties. Important question types include:
- Finding the angle between two vectors.
- Calculating the projection of one vector onto another.
- Problems where you are given that two vectors are perpendicular (i.e., their dot product is zero) and you need to find an unknown value. For example, if vector a = 2i + λj + k and vector b = i - 2j + 3k are perpendicular, find λ.
- Questions involving properties like |a + b|² = |a|² + |b|² + 2(a · b).
3. What kind of 5-mark or long-answer questions are considered important from Chapter 10, Vector Algebra?
Five-mark questions from Vector Algebra are usually application-based and may combine multiple concepts. Some of the most important types for the 2025-26 exam are:
- Finding a vector that is perpendicular to two given vectors and satisfies another condition (e.g., has a specific magnitude or a given dot product with a third vector). This involves using the cross product.
- Questions on the scalar triple product, such as proving that three vectors are coplanar or finding the volume of a parallelepiped whose adjacent edges are given vectors.
- Problems that require you to express a vector as the sum of two other vectors—one that is parallel to a given vector and another that is perpendicular to it.
4. What types of 1-mark or MCQ questions are expected from Vector Algebra in the board paper?
For the 1-mark section, expect direct and formula-based questions. Important types include:
- Finding the magnitude of a vector.
- Calculating the unit vector in the direction of a given vector.
- Determining the direction cosines of a vector.
- Simple applications of the dot product to find if vectors are orthogonal (perpendicular).
- Basic questions on the condition for two vectors being parallel (collinear).
5. Why is the concept of coplanarity of vectors an important area for board exam questions?
The concept of coplanarity is a favourite for examiners because it effectively tests a student's understanding of the scalar triple product and its geometric meaning. A question on coplanarity isn't just about calculation; it checks if you know that the scalar triple product of three coplanar vectors, [a b c], is zero because the volume of the parallelepiped formed by them is zero. This makes it a great topic for HOTS (Higher-Order Thinking Skills) questions where you might need to prove coplanarity to solve a larger problem.
6. How can a student avoid common mistakes in questions asking to find the area of a parallelogram or triangle using vectors?
This is a critical area where students often lose marks. To avoid mistakes:
- For a Parallelogram: If the adjacent sides are given as vectors a and b, the area is |a × b|. However, if the diagonals are given as vectors d₁ and d₂, the area is ½ |d₁ × d₂|. Students often confuse these two formulas.
- For a Triangle: If two adjacent sides are vectors a and b, the area is ½ |a × b|. If the position vectors of the vertices A, B, and C are given, first find the vectors representing two sides (e.g., AB and AC) and then apply the formula.
7. In what exam scenarios is it better to use the dot product versus the cross product to find the angle between two vectors?
This is an important strategic point for exams.
- You should almost always use the dot product (cos θ = (a · b) / (|a| |b|)) to find the angle between two vectors. It is computationally simpler as it results in a scalar.
- The cross product formula (sin θ = |a × b| / (|a| |b|)) is more complex to compute and gives sin θ, which can lead to ambiguity (e.g., sin 30° = sin 150°).
