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Vector Algebra Practice Questions

JEE · Mathematics · 1528 free MCQs with instant results and detailed explanations.

1528
Total
372
Easy
704
Medium
452
Hard

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Topics in Vector Algebra

Vector Triple Product 203
Applications of Vectors 232
Types of Vectors 324
Scalar Triple Product 316
Cross Product 342
Dot Product 111

Sample Questions from Vector Algebra

Here are 10 sample questions. Start a quiz to get randomized questions with scoring.

Q1
Easy
Which of the following is a zero vector?
A. (0, 0, 0)
B. (1, 1, 1)
C. (2, 2, 2)
D. (3, 3, 3)
Show Answer & Explanation
Correct Answer: A
The zero vector has all its components equal to zero. Hence, (0, 0, 0) is the zero vector.
Q2
Easy
Which of the following vectors is a unit vector?
A. (2, 0, 0)
B. (0, 1, 0)
C. (1/√2, 1/√2, 0)
D. (0, 0, 0)
Show Answer & Explanation
Correct Answer: C
A unit vector has a magnitude of 1. The magnitude of (1/√2, 1/√2, 0) is √(1/2 + 1/2) = 1.
Q3
Easy
If vector A = (3, 4) and vector B = (1, -2), what is A + B?
A. (4, 2)
B. (2, 2)
C. (5, 6)
D. (3, 6)
Show Answer & Explanation
Correct Answer: A
Adding vectors involves adding their corresponding components. (3 + 1, 4 - 2) = (4, 2).
Q4
Medium
Which of the following vectors is a unit vector?
A. Vector A = (3, 4)
B. Vector B = (1, 0)
C. Vector C = (0, 0)
D. Vector D = (2, -2)
Show Answer & Explanation
Correct Answer: B
A unit vector has a magnitude of 1. Vector B has a magnitude of 1, while all others do not.
Q5
Medium
Two vectors A and B are equal if which of the following conditions hold true?
A. A + B = 0
B. A - B = A
C. A + B = A + A
D. A = B
Show Answer & Explanation
Correct Answer: D
Two vectors A and B are equal if they have the same magnitude and direction, which is expressed as A = B.
Q6
Medium
Which of the following vectors is a null vector?
A. (1, 1)
B. (0, 0)
C. (5, 5)
D. (-1, -1)
Show Answer & Explanation
Correct Answer: B
A null vector is a vector with zero magnitude, represented by (0, 0).
Q7
Medium
What is the angle between two vectors A = (1, 2) and B = (2, 3) if their dot product is 0?
A. 0 degrees
B. 90 degrees
C. 180 degrees
D. 45 degrees
Show Answer & Explanation
Correct Answer: B
If the dot product is zero, the vectors are orthogonal, which means the angle between them is 90 degrees.
Q8
Hard
Which of the following is NOT a property of unit vectors?
A. They have a magnitude of 1.
B. They can be added to form other vectors.
C. They are always parallel to each other.
D. They can represent direction.
Show Answer & Explanation
Correct Answer: C
Unit vectors can point in any direction and are not necessarily parallel.
Q9
Hard
Which of the following statements about position vectors is true?
A. The position vector always has a zero magnitude.
B. Position vectors can be negative.
C. Position vectors indicate the location of a point in space.
D. Position vectors are always perpendicular to each other.
Show Answer & Explanation
Correct Answer: C
Position vectors describe the position of points relative to the origin.
Q10
Hard
If vectors A and B are orthogonal, which relationship holds true?
A. A·B = 1
B. A·B = 0
C. |A| = |B|
D. A × B = 0
Show Answer & Explanation
Correct Answer: B
Two vectors are orthogonal when their dot product equals zero.

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Vector Algebra — JEE Mathematics Practice Questions Online

This page contains 1528 practice MCQs for the chapter Vector Algebra in JEE Mathematics. The questions are organized by difficulty — 372 easy, 704 medium, 452 hard — so you can choose the right level for your preparation.

Every question includes a detailed explanation to help you understand the concept, not just memorize answers. Take a timed quiz to simulate exam conditions, or practice at your own pace with no time limit. This chapter covers 6 topics, giving you comprehensive coverage of the entire chapter.