WBJEE 2025 Vector Algebra Practice Questions with Solutions

WBJEE 2025 Vector Algebra Practice Questions with Solutions: If you are aiming to score 90+ in WBJEE exam 2025, then you should not skip the Vector Algebra chapter as it carries a significant weightage of approximately 7%. It is often considered an easier topic to cover during the WBJEE 2025 exam preparation. To prepare well for this chapter, you should diligently solve WBJEE 2025 Vector Algebra practice questions on the addition of vectors, dot and cross products of vectors etc. Since the topic is common to both the West Bengal 12th Boards curriculum and the WBJEE 2025 syllabus PDF , you must already be familiar with the fundamental concepts and the application of formula. However, to take your exam preparation a step ahead, review the list of WBJEE 2025 Vector Algebra practice questions with solutions shared by our experts.

Also Check - Is Class 12 Syllabus Enough for WBJEE?

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List of WBJEE 2025 Vector Algebra Sub Topics for Exam Preparation

The chapter on Vector Algebra covers various fundamental concepts from Vector Theory such as addition and multiplication. The WBJEE 2025 Mathematics syllabus PDF provides all the topics and sub topics that will be asked in the question paper. The following table includes the complete list of Vector Algebra sub topics that you need to practice for the upcoming WBJEE exam 2025.

WBJEE 2025 Vector Algebra Expected Weightage

The Vector Algebra marks weightage helps you assess the importance of the chapter and the topics. As per the previous years' paper format, around 4-5 questions, each carrying one mark or two marks, will be asked from this section. So you have a fair chance of scoring at least 5-10 marks in the Vector Algebra part. Let’s have a look at the expected WBJEE 2025 Vector Algebra marks weightage in the table below.

WBJEE 2025 Vector Algebra Practice Questions with Solutions

Solving WBJEE 2025 Vector Algebra practice questions daily will help you improve your problem-solving skills and boost overall exam preparation. After analyzing WBJEE 10 years solved papers, our experts have compiled a series of WBJEE 2025 Vector Algebra practice questions with solutions so that you can get used to the paper format. These practice question papers will also help you to improve your speed and efficiency under timed conditions. Check out some of the helpful Vector Algebra practice questions with solutions for WBJEE 2025 in this section.

Q1. Find the position vector of a point that divides the join of points with position vectors a⃗ −2b⃗  and 22a⃗ +b⃗  externally in the ratio 2:1.

a. 3a⃗  + 4 b⃗

b. 3a⃗  - 4 b⃗

c. a⃗  + b⃗

d. None of the above

Ans. a. 3a⃗ + 4 b⃗

Solution:

Let the given position of vector OA=a⃗ −2b⃗  and vector OB = 2a⃗ +b⃗

Let OA be the position vector of a point C which divides the join of points, with position vectors OA and OB, externally in the ratio 2:1.

OA = (2OB−1OA)/(2−1)

2(2a⃗ +b⃗ )−1(a⃗ −2b⃗ )/1 [by external section formula]

= 4a⃗  + 2b⃗  – a⃗  + 2b⃗  = 3a⃗  + 4b⃗.

Q2. If a⃗  = 4î – ĵ + k̂ and b⃗  = 2î – 2ĵ + k̂, then find a unit vector parallel to the vector a⃗ +b⃗.

a. 1/8(6î−3ĵ +2k̂)

b. 1/7(6î−3ĵ +2k̂)

c. 1/7((6î−3ĵ +2k̂)

d. (6î−3ĵ +2k̂)

Ans. b. 1/7(6î−3ĵ +2k̂)

Solution:

To find a unit vector parallel to the vector a ^→ +b ^→ , we will follow these steps:

Step 1: Find a⃗ +b⃗

Given:

a⃗=4î−ĵ+k̂

b⃗=2î−2ĵ+k̂

Now, we add the both vectors:

6î−3ĵ+2k̂

Step 2: Calculate the magnitude of a⃗ +b⃗

|v|=√x2+y2+z2

|a+b|=√(6)2+(−3)2+(2)2 =7

Step 3: Find the unit vector parallel to a⃗ +b⃗

A unit vector in the direction of a vector v is given by:

u = v/[v]

Thus, the unit vector parallel to a⃗ +b⃗ is:

6/7î + 3/7ĵ + 2/7k̂

= 1/7(6î−3ĵ +2k̂).

Q3. let α, β, γ be three non-zero vectors which are pairwise non-collinear. if  α+ 3β is collinear with γ and β + 2γ is collinear with α then α + 3β + 6γ is:

a. γ

b. 0

c. γ + γ

d. α

Ans. b. 0

Solution:

Given, α+ 3β is collinear with γ

∴ α+ 3β = λγ ….. (1)

and β + 2γ is collinear with α

∴ β + 2γ = μα ….. (2)

Add 6γ to the equation (1) we get,

α+ 3β + 6γ = (6 + λ)γ ….. (3)

Multiply equation (2) with (3) and add α

α+ 3β + 6γ = (3μ + 1)α ….. (4)

From (3) and (4) we get,

(6 + λ)γ = (3μ + 1)α ….. (5)

As α, β, γ are not pairwise collinear so in equation (5), the coefficient of γ and α must be zero

6 + λ = 0 and 3μ + 1 = 0

From equation (3)

λ + 3β + 6γ = (6+λ)γ = 0 x γ = 0.

Q4. If a (α x β) + b (β x γ) + c(γ x α) = 0 where a, b, c are non-zero scalars, then the vectors α, β, γ are:

a. Parallel

b. Non-coplanar

c. Coplanar

d. Multi Perpendicular

Ans. c. Coplanar

Solution:

Given, a (α x β) + b (β x γ) + c(γ x α) = 0

Thus, a (α x β), b (β x γ), c(γ x α) are coplanar vector

∴ α, β, γ are also coplanar

Q5. If the sum of two unit vectors is a unit vector, then the magnitude of their difference is

a. √2 units

b. 2 units

c. √3 units

d. √5 units

Ans. c. √3 units

Q6. The position vectors of points A, B, C, and D are 3î − 2ĵ – k̂, 2î − 3ĵ + 2k̂, 5î − ĵ + 2k̂, and 4î−ĵ–λk̂, respectively. If the points A, B, C, and D lie on a plane, the value of λ is:

a. 0

b. 1

c. 2

d. – 4

Ans. d. – 4

Q7. If α is a unit vector, β ^→ = î+ĵ–k̂, γ ^→ = î+k̂ then the maximum value of [α ^→ β ^→ γ ^→ ] is:

a. 3

b. √3

c. 2

d. √6

Ans. d. √6

Q8. The value of 'a' for which the scalar triple product formed by the vectors α ^→ = î+aĵ+k̂, β ^→ = ĵ+ak̂, and γ ^→ = aî+k̂, is maximum, is

a. 3

b. –3

c. – 1/√3

d. 1/√3

Ans. c. – 1/√3

Q9. If the volume of the parallelopiped with a ^→ x b ^→, b ^→ x c ^→ , and c ^→ x a ^→ as conterminous edges is 9 cu. units, then the volume of the parallelopiped with (a ^→ x b ^→ ) x (b ^→ x c ^→ ), (b ^→ x c ^→ ) x (c ^→ x a ^→ ), and (c ^→ x a ^→ ) x (a ^→ x b ^→ ) as conterminous edges is

a. 9 cu. units

b. 729 cu. units

c. 81 cu. units

d. 243 cu. units

Ans. c. 81 cu. units

Q10. If a ^→ = î+ĵ-k̂, b ^→ = î-ĵ+k̂ and c ^→ is unit vector perpendicular to a ^→ and coplanar with a ^→ and b ^→ , then unit vector d ^→ perpendicular to both a ^→ and c ^→ is

a. 士 1/√6 (2î-ĵ+k̂)

b. 士 1/√2 (ĵ+k̂)

c. 士 1/√6 (î-2ĵ+k̂)

d. 士 1/√2 (ĵ-k̂)

Ans. b. 士 1/√2 (ĵ+k̂)

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The WBJEE 2025 Vector Algebra practice questions serve as model question papers. By solving these questions regualrly, you can identfiy and work on your mistakes and adopt the right approach when solving the exam paper. You can further enhance your exam preparation by taking the chapter-wise WBJEE 2025 mock test alongside sample papers.

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