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Vector Algebra Practice Questions

Class 12 · Mathematics · 1532 free MCQs with instant results and detailed explanations.

1532
Total
630
Easy
657
Medium
245
Hard

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Topics in Vector Algebra

Addition of Vectors 380
Scalar and Vector Product 329
Types of Vectors 823

Sample Questions from Vector Algebra

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

Q1
Easy
What type of vector has a magnitude but no direction?
A. Scalar
B. Vector
C. Unit Vector
D. Zero Vector
Show Answer & Explanation
Correct Answer: A
A scalar only has magnitude, such as temperature or mass, and does not have a direction.
Q2
Easy
Which of the following is an example of a unit vector?
A. 3i + 4j
B. i
C. 2i + 2j
D. 5i + 12j
Show Answer & Explanation
Correct Answer: B
A unit vector has a magnitude of 1, and 'i' represents a unit vector along the x-axis.
Q3
Easy
Which vector has both magnitude and direction?
A. Scalar
B. Zero Vector
C. Vector
D. Unit Scalar
Show Answer & Explanation
Correct Answer: C
A vector has both a defined magnitude and direction, unlike a scalar which has only magnitude.
Q4
Medium
Which of the following vectors is considered a zero vector?
A. 0i + 0j
B. 1i + 0j
C. 0i + 1j
D. -1i + -1j
Show Answer & Explanation
Correct Answer: A
The zero vector has no magnitude and direction, represented as 0i + 0j.
Q5
Medium
Which of the following vectors is a unit vector?
A. 2i
B. 3j
C. 1/√2 i + 1/√2 j
D. 4i + 4j
Show Answer & Explanation
Correct Answer: C
A unit vector has a magnitude of 1. The vector C has magnitude 1.
Q6
Medium
If vectors A and B are parallel, what is the angle between them?
A. 0°
B. 90°
C. 180°
D. 45°
Show Answer & Explanation
Correct Answer: A
Parallel vectors have an angle of 0° or 180° depending on their direction.
Q7
Medium
Which vector represents a vector in the opposite direction of vector A = 5i - 2j?
A. -5i + 2j
B. 5i + 2j
C. -5i - 2j
D. 5i - 2j
Show Answer & Explanation
Correct Answer: A
The opposite vector is obtained by negating each component of vector A.
Q8
Hard
Which of the following pairs of vectors are unit vectors?
A. A = 4i + 3j, B = -3i - 4j
B. A = i + 0j, B = 0i + j
C. A = 5i + 12j, B = -12i + 5j
D. A = 2i + 2j, B = -2i + 2j
Show Answer & Explanation
Correct Answer: B
Unit vectors have a magnitude of 1. Vectors A = i + 0j and B = 0i + j each have a magnitude of 1, while other options do not.
Q9
Hard
If vectors A = a i + b j and B = c i + d j are equal, which of the following must be true?
A. a + d = c + b
B. a = c and b = d
C. a + b = c + d
D. a^2 + b^2 = c^2 + d^2
Show Answer & Explanation
Correct Answer: B
Two vectors are equal if their corresponding components are equal. Therefore, a must equal c and b must equal d.
Q10
Hard
Which of the following is a unit vector?
A. (3, 4, 0)
B. (1/√2, 1/√2, 0)
C. (2, 0, 0)
D. (0, -1, 1)
Show Answer & Explanation
Correct Answer: B
A unit vector has a magnitude of 1. (1/√2, 1/√2, 0) has a magnitude of 1.

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Vector Algebra — Class 12 Mathematics Practice Questions Online

This page contains 1532 practice MCQs for the chapter Vector Algebra in Class 12 Mathematics. The questions are organized by difficulty — 630 easy, 657 medium, 245 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 3 topics, giving you comprehensive coverage of the entire chapter.