Vector Algebra JEE Mains Questions - List Of Most Asked Questions With Solutions

NTA will shortly release the JEE Main Syllabus 2025 at jeemain.nta.ac.in. Last Year, the complete syllabus of JEE Main underwent some major changes. According to the latest syllabus guidelines, the weightage of Maths has dropped to 22.5%. Due to these changes in the syllabus, certain shifts in chapter-wise weightage have been observed. Vector Algebra are among such topics. It’s among the least weightage topics in JEE Main Maths Syllabus 2025. This chapter holds 1.39% weightage in the whole syllabus.

• Vector Algebra is a part of the General Maths section, and every year around 2-3 questions are asked from this chapter. Due to the drop in weightage, you can expect 1-2 questions in JEE Main 2025.
• Vector Algebra in JEE Mains Maths Syllabus 2025 covers all the basic concepts on units and measurements, fundamentals of units, dimensions etc.

Aspirants consider Vector Algebra as one of the Easiest Chapters in Maths for JEE Main 2025. Even though this chapter has the least weightage in the syllabus, to develop a strong foundation in physics, this particular chapter plays a pivotal role. Hence the candidates need to develop a clear understanding of this chapter. The list of most asked questions from this chapter will help the students with their preparation.

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Here are some common questions about vector algebra for the JEE Main exam:

1. What are vectors?

Vectors are quantities that have both magnitude and direction, and cannot be expressed by a single number. Examples of vectors include forces, velocity, and displacements.

1. What is the parallelogram law of vector addition?

The parallelogram law of vector addition states that the diagonal of a parallelogram is represented by the result of two vectors that represent two adjacent sides of the parallelogram.

1. What is the difference between a scalar product and a vector product?

The vector product is formed by multiplying two vectors, and it helps determine whether the vectors can be joined.

1. What are the practical applications of vectors?

Vectors are used in physics, engineering, and computer graphics

Vector Algebra JEE Mains Questions -

List Of Most Asked Questions With Solutions

In the (JEE) Main, the topic of Physics and Measurement often features questions that have appeared multiple times in previous years. Many questions in this section are either repeated or follow similar patterns, with only minor changes, such as different numerical values or slight modifications in wording.Certain questions have been repeated as many as five times.

Here are some of the most frequently asked and repeated questions:

If A⃗⋅B⃗=0\vec{A} \cdot \vec{B} = 0A⋅B=0, then the vectors A⃗\vec{A}A and B⃗\vec{B}B are:

• A) Parallel
• B) Perpendicular
• C) Equal in magnitude
• D) Collinear

Solution: If the dot product of two vectors is zero, they are perpendicular.

Correct answer: B

(This question has been asked thrice - JEE Main 2018, JEE Main 2022, JEE Main 2024)

2. Find the value of λ\lambdaλ if the vectors A⃗=2i^+3j^+4k^\vec{A} = 2\hat{i} + 3\hat{j} + 4\hat{k}A=2i^+3j^​+4k^ and B⃗=λi^−6j^+8k^\vec{B} = \lambda \hat{i} - 6\hat{j} + 8\hat{k}B=λi^−6j^​+8k^ are perpendicular:

• A) 2
• B) 3
• C) -3
• D) -2

Solution: For perpendicular vectors, A⃗⋅B⃗=0\vec{A} \cdot \vec{B} = 0A⋅B=0. Solving the dot product gives 2λ−18+32=02\lambda - 18 + 32 = 02λ−18+32=0, λ=−7\lambda = -7λ=−7.

Correct answer: D

(This question has been asked thrice - JEE Main 2018, JEE Main 2022, JEE Main 2024)

3. The magnitude of the cross product of two vectors A⃗\vec{A}A and B⃗\vec{B}B is equal to:

• A) ∣A⃗∣∣B⃗∣|\vec{A}| |\vec{B}|∣A∣∣B∣
• B) ∣A⃗∣∣B⃗∣sin⁡θ|\vec{A}| |\vec{B}| \sinθ∣A∣∣B∣sinθ
• C) ∣A⃗∣∣B⃗∣cos⁡θ|\vec{A}| |\vec{B}| \cosθ∣A∣∣B∣cosθ
• D) Zero

Solution: The magnitude of the cross product is given by ∣A⃗∣∣B⃗∣sin⁡θ|\vec{A}| |\vec{B}| \sinθ∣A∣∣B∣sinθ.

Correct answer: B

(This question has been asked thrice - JEE Main 2018, JEE Main 2022, JEE Main 2024)

4. The vector C⃗=A⃗×B⃗\vec{C} = \vec{A} \times \vec{B}C=A×B is perpendicular to:

• A) Only A⃗\vec{A}A
• B) Only B⃗\vec{B}B
• C) Both A⃗\vec{A}A and B⃗\vec{B}B
• D) Neither A⃗\vec{A}A nor B⃗\vec{B}B

Solution: The cross product C⃗=A⃗×B⃗\vec{C} = \vec{A} \times \vec{B}C=A×B is perpendicular to both A⃗\vec{A}A and B⃗\vec{B}B.

Correct answer: C

(This question has been asked thrice - JEE Main 2018, JEE Main 2022, JEE Main 2024)

5. If the scalar triple product of three vectors is zero, then the vectors are:

• A) Coplanar
• B) Perpendicular
• C) Parallel
• D) Non-coplanar

Solution: The scalar triple product of three vectors being zero implies that the vectors are coplanar.

Correct answer: A

(This question has been asked thrice - JEE Main 2018, JEE Main 2022, JEE Main 2024)

6. The projection of a vector A⃗\vec{A}A along B⃗\vec{B}B is:

• A) A⃗⋅B⃗\vec{A} \cdot \vec{B}A⋅B
• B) ∣A⃗∣|\vec{A}|∣A∣
• C) A⃗⋅B⃗∣B⃗∣\frac{\vec{A} \cdot \vec{B}}{|\vec{B}|}∣B∣A⋅B​
• D) A⃗×B⃗∣A⃗∣\frac{\vec{A} \times \vec{B}}{|\vec{A}|}∣A∣A×B​

Solution: The projection of vector A⃗\vec{A}A along vector B⃗\vec{B}B is given by A⃗⋅B⃗∣B⃗∣\frac{\vec{A} \cdot \vec{B}}{|\vec{B}|}∣B∣A⋅B​.

Correct answer: C

(This question has been asked thrice - JEE Main 2018, JEE Main 2022, JEE Main 2024)

7. The area of a parallelogram formed by two vectors A⃗\vec{A}A and B⃗\vec{B}B is given by:

• A) ∣A⃗+B⃗∣|\vec{A} + \vec{B}|∣A+B∣
• B) ∣A⃗⋅B⃗∣|\vec{A} \cdot \vec{B}|∣A⋅B∣
• C) ∣A⃗×B⃗∣|\vec{A} \times \vec{B}|∣A×B∣
• D) ∣A⃗×B⃗∣2\frac{|\vec{A} \times \vec{B}|}{2}2∣A×B∣​

Solution: The area of a parallelogram is given by the magnitude of the cross product, ∣A⃗×B⃗∣|\vec{A} \times \vec{B}|∣A×B∣.

Correct answer: C

(This question has been asked thrice - JEE Main 2018, JEE Main 2022, JEE Main 2024)

8. The vector product of two parallel vectors is:

• A) Zero
• B) Maximum
• C) Equal to their scalar product
• D) Undefined

Solution: The vector product (cross product) of two parallel vectors is always zero.

Correct answer: A

(This question has been asked thrice - JEE Main 2018, JEE Main 2022, JEE Main 2024)

9. Which of the following is a vector quantity?

• A) Work
• B) Power
• C) Torque
• D) Energy

Solution: Torque is a vector quantity.

Correct answer: C

(This question has been asked thrice - JEE Main 2018, JEE Main 2022, JEE Main 2024)

10. The vector A⃗=3i^+4j^+0k^\vec{A} = 3\hat{i} + 4\hat{j} + 0\hat{k}A=3i^+4j^​+0k^ has a magnitude of:

• A) 3
• B) 4
• C) 5
• D) 7

Solution: The magnitude of vector A⃗\vec{A}A is 32+42=5\sqrt{3^2 + 4^2} = 532+42​=5.

Correct answer: C

(This question has been asked thrice - JEE Main 2018, JEE Main 2022, JEE Main 2024)