COMEDK UGET 2025 Vector Algebra Practice Questions with Solutions

COMEDK UGET 2025 Vector Algebra Practice Practice Questions with Solutions: Vector Algebra is one of the most important chapters in COMEDK exam syllabus. This section covers around 15% of weightage in COMEDK UGET 2025 exam. If you are preparing for the exam, you should start solving COMEDK UGET 2025 Vector Algebra practice questions to boost your preparation. Practicing with COMEDK Vector Algebra sample questions will give you an idea of the type of questions and topics expected to appear in the exam paper. While the section will majorly cover formula-based questions, you would be able to understand where and when to apply them by regularly solving these practice questions. Alongside, you should study the complete COMEDK UGET 2025 Mathematics syllabus and identify important topics to plan your exam preparation plan. In this article, we have provided some of the most important and expected COMEDK UGET 2025 Vector Algebra practice questions with solutions so you can go through the explanations and logic behind the correct answers.

Also Check - Do or Die Chapters for COMEDK UGET 2025 Mathematics

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COMEDK UGET 2025 Vector Algebra Important Topics

COMEDK UGET 2025 Vector Algebra chapter covers several important topics such as Vector and Scalars, Direction Cosines, and position vector. In the following table, we have provided all the topics mentioned in the COMEDK 2025 syllabus:

COMEDK UGET 2025 Vector Algebra Expected Weightage

COMEDK 2025 Vector Algebra expected weightage will help you assess how many questions will be covered from this topic. Generally, the weightage of COMEDK Vector Algebra is around 15-16%. Therefore, you can expect around 9 to 10 questions from this chapter. In the following table, we have provided the expected COMEDK UGET 2025 Vector weightage:

COMEDK UGET 2025 Vector Algebra Practice Questions with Solutions

COMEDK chapter wise PYQ for Mathematics plays an essential part in scoring good marks, understanding the question pattern and difficulty level. Without solving Vector Algebra practice questions for COMEDK, you will not be able to evaluate your preparation and progress no matter how much you study. Therefore, for a holistic exam preparation, we have shared some of the most expected questions for COMEDK Vector Algebra from the past years' papers. Go through the important COMEDK UGET 2025 Vector Algebra practice questions with solutions, see how many you can solve easily, and work on your shortcomings. 

Q1. The vector that must be added to î - 3ĵ + 2k̂ and 3î + 6ĵ - 7k̂ so the resultant vector is a unit vector along the X-axis is

a. - 3î - 3ĵ + 5k̂

b. -4î + 2ĵ + 5k̂

c. 3î + 4ĵ + 5k̂

d. Null Vector

Ans.a. - 3î - 3ĵ + 5k̂

Solution: Let the vector be, xî + yĵ + zk̂

Since the unit vector along X is î

î = V1 + V2 + V3

Simplifying this equation we get, 

x = -3, y = - 3, and z = 5

Thus, the correct answer is, - 3î - 3ĵ + 5k̂.

Q2. If |a| = 8, |b| = 3 and |a x b| = 12, then find the angle between a and b

a. ⲡ/3

b. ⲡ/4

c. ⲡ/6

d. ⲡ/2

Ans.c. ⲡ/6

Solution: We know SinΘ = |axb||a||b|

We are given, |a| = 8, |b| = 3 and |a x b| = 12

Then from the above given expression,

SinΘ = ⲡ/6.

Q3. f a and b are vectors such that |a + b| = |a - b|, the the angle between a and b is:

a. 60°

b. 120°

c. 90°

d. 30°

Ans. c. 90°

Solution: |a + b| = |a - b| 

|a + b|² = |a - b|²

(a+b).(a+b) = (a-b).(a-b)

a² + b² + 2a.b = a² + b² - 2a.b

4a.b = 0

a.b = 0

So, the angle between a and b is 90°.

Q4. If x, y and z are non-zero real numbers and a = xî + 2k̂, b = yĵ + 3k̂, and c = xî + yĵ + zk̂ are such that a x b = zî - 3ĵ + k̂ then [a b c] is equal to:

a. 10

b. 9

c. 3

d. 6

Ans. b. 9

Solution: Given, a = xî + 2k̂, b = yĵ + 3k̂, and c = xî + yĵ + zk̂

a x b =

Then, î(6 - 0) - ĵ(3x - 0) + k̂(xy - 0)

Simplifying this we get, 

zî - 3ĵ + k̂

On equating the coefficients

z = 6, x = 1, and xy = 1, so y = 1

Now, [a b c] =

[a b c] = 1(6 - 3) - 2(0 - 3) + 0 = 9

Q5. If p = î + ĵ, q = 4k̂ - ĵ, and r = î + k̂, then the unit vector in the direction of 3p + q - 2r is:

a. ⅓ (î + 2ĵ + 2k̂)

b. ⅓ (î - 2ĵ - 2k̂)

c. ⅓(î + 2ĵ - 2k̂)

d. None of the above

Ans.a. ⅓ (î + 2ĵ + 2k̂)

Solution: 3p + q - 2r 

3(î + ĵ) + (4k̂ - ĵ) - 2(î + k̂)

Î + 2ĵ + 2k̂

Unit vector in the direction of

3p + q - 2r = ⅓ (î + 2ĵ + 2k̂)

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