What is Exam Sprinter?

Exam Sprinter is an AI-powered platform designed for competitive exam preparation like UPSC, JEE, NEET, and SSC. It offers personalized study plans, unlimited practice questions, and real-time AI tutoring.

How does Exam Sprinter help with preparation?

Exam Sprinter uses AI to create personalized study plans based on your strengths and weaknesses. You get access to unlimited AI-generated mocks, deep analytics, and 24/7 AI tutor support for instant doubt resolution.

Is Exam Sprinter free to use?

Yes, Exam Sprinter offers free access to start your preparation for exams like JEE, NEET, SSC, and UPSC. Download the app to drop in and start learning.

Vector Algebra MCQs (Free Practice Questions)

Practice 10 carefully selected Vector Algebra MCQs with explanations. Continue practicing 500+ chapter-wise questions inside the Exam Sprinter app.

What is Vector Algebra?

Vector Algebra covers the essential principles and concepts required for NDA.

💡 Why Study Vector Algebra?

Highly important, frequently tested in NDA.

Parameter	Details / Relevance
Target Exam	NDA
Subject Category	Mathematics
Recommended Study Duration	10 Hours
Expected Questions	2 Questions
Difficulty Index	Hard
Interactive Solved MCQs	10 Questions (Complete Explanations)
Adaptive App Practice	500+ Questions & AI Tutor Supported

⚠️ Common Pitfalls to Avoid

Neglecting foundational prerequisites (make sure you review related chapters in the learning path).
Calculation and sign convention errors during numerical steps.
Confusing intermediate results with the final correct answer options.

🗺️ Recommended learning path

Integral Calculus➔Vector Algebra (Current)➔Statistics

What You Will Learn

✓ Vector Algebra Fundamentals
✓ Key applications of Vector Algebra
✓ Advanced problem solving in Vector Algebra

Cheat Sheet & Formulas

$$\sin^2 x + \cos^2 x = 1$$
$$\vec{a} \cdot \vec{b} = ab \cos\theta$$

Practice Questions

⏱ 60sHard

If a matrix $A$ of order $3 \times 3$ has determinant $|A| = 7$ , then find the determinant of $2A$ .

⏱ 65sMedium

Find the value of $\sin(15^\circ) + \cos(105^\circ)$ for Vector Algebra.

⏱ 70sEasy

Find the principal argument of the complex number $z = 4 + 4i$ .

⏱ 75sHard

If vectors $\vec{a} = 7\vec{i} - \vec{j} + \vec{k}$ and $\vec{b} = \vec{i} + 1\vec{j} + \lambda\vec{k}$ are perpendicular, find the value of $\lambda$ .

⏱ 80sMedium

What is the probability of getting a sum of 11 when two fair dice are thrown?

⏱ 85sEasy

The derivative of $\ln(\sin(2x))$ with respect to $x$ is:

⏱ 90sHard

Evaluate the limit: $\lim_{x \to 0} \frac{\tan(7x)}{x}$ for Vector Algebra.

⏱ 95sMedium

The coordinates of the focus of the parabola $y^2 = 32x$ are:

⏱ 100sEasy

Find the number of subsets of a set containing 3 elements.

Q10

⏱ 105sHard

The vector projection of $\vec{a} = \vec{i} + \vec{j}$ on $\vec{b} = \vec{i} - \vec{j}$ is:

Chapter Guide ✓→Formulas ✓→10 Questions ✓→Next: 500+ Questions in App

Want to master Vector Algebra?

You've just completed 10 questions. Continue practicing in the Exam Sprinter app to reach mastery.

📱Offline Practice

🤖AI-Powered Learning

📚100,000+ Questions

⭐Highly Rated on Google Play

Frequently Asked Questions

Is Vector Algebra difficult for the exam?▼

Yes, Vector Algebra requires strong conceptual clarity and practice of standard NDA style questions.

✓ Key Takeaways for Vector Algebra

High exam relevance: 2 questions on average are expected from this chapter.
Standard formulas: Comprehensive formula sheets and formulas are fully covered in the cheat sheet section above.
Practice and explanation: 10 standard MCQs are solved step-by-step to clarify common numerical and conceptual methods.
Step-by-step learning: Start with the formulas, work through the questions, and then download the mobile app for extensive practice.

Vector Algebra MCQs (Free Practice Questions)

🤖 Quick AI Summary

What is Vector Algebra?

💡 Why Study Vector Algebra?

⚠️ Common Pitfalls to Avoid

🗺️ Recommended learning path

What You Will Learn

Cheat Sheet & Formulas

Practice Questions

If a matrix $A$ of order $3 \times 3$ has determinant $|A| = 7$ , then find the determinant of $2A$ .

Find the value of $\sin(15^\circ) + \cos(105^\circ)$ for Vector Algebra.

Find the principal argument of the complex number $z = 4 + 4i$ .

If vectors $\vec{a} = 7\vec{i} - \vec{j} + \vec{k}$ and $\vec{b} = \vec{i} + 1\vec{j} + \lambda\vec{k}$ are perpendicular, find the value of $\lambda$ .

What is the probability of getting a sum of 11 when two fair dice are thrown?

The derivative of $\ln(\sin(2x))$ with respect to $x$ is:

Evaluate the limit: $\lim_{x \to 0} \frac{\tan(7x)}{x}$ for Vector Algebra.

The coordinates of the focus of the parabola $y^2 = 32x$ are:

Find the number of subsets of a set containing 3 elements.

The vector projection of $\vec{a} = \vec{i} + \vec{j}$ on $\vec{b} = \vec{i} - \vec{j}$ is:

Want to master Vector Algebra?

Frequently Asked Questions

✓ Key Takeaways for Vector Algebra

🔗 Related Study Resources

Vector Algebra MCQs (Free Practice Questions)

🤖 Quick AI Summary

What is Vector Algebra?

💡 Why Study Vector Algebra?

⚠️ Common Pitfalls to Avoid

🗺️ Recommended learning path

What You Will Learn

Cheat Sheet & Formulas

Practice Questions

If a matrix AAA of order 3×33 \times 33×3 has determinant ∣A∣=7|A| = 7∣A∣=7, then find the determinant of 2A2A2A.

Find the value of sin⁡(15∘)+cos⁡(105∘)\sin(15^\circ) + \cos(105^\circ)sin(15∘)+cos(105∘) for Vector Algebra.

Find the principal argument of the complex number z=4+4iz = 4 + 4iz=4+4i.

If vectors a⃗=7i⃗−j⃗+k⃗\vec{a} = 7\vec{i} - \vec{j} + \vec{k}a=7i−j​+k and b⃗=i⃗+1j⃗+λk⃗\vec{b} = \vec{i} + 1\vec{j} + \lambda\vec{k}b=i+1j​+λk are perpendicular, find the value of λ\lambdaλ.

What is the probability of getting a sum of 11 when two fair dice are thrown?

The derivative of ln⁡(sin⁡(2x))\ln(\sin(2x))ln(sin(2x)) with respect to xxx is:

Evaluate the limit: lim⁡x→0tan⁡(7x)x\lim_{x \to 0} \frac{\tan(7x)}{x}x→0lim​xtan(7x)​ for Vector Algebra.

The coordinates of the focus of the parabola y2=32xy^2 = 32xy2=32x are:

Find the number of subsets of a set containing 3 elements.

The vector projection of a⃗=i⃗+j⃗\vec{a} = \vec{i} + \vec{j}a=i+j​ on b⃗=i⃗−j⃗\vec{b} = \vec{i} - \vec{j}b=i−j​ is:

Want to master Vector Algebra?

Frequently Asked Questions

✓ Key Takeaways for Vector Algebra

🔗 Related Study Resources

If a matrix $A$ of order $3 \times 3$ has determinant $|A| = 7$ , then find the determinant of $2A$ .

Find the value of $\sin(15^\circ) + \cos(105^\circ)$ for Vector Algebra.

Find the principal argument of the complex number $z = 4 + 4i$ .

If vectors $\vec{a} = 7\vec{i} - \vec{j} + \vec{k}$ and $\vec{b} = \vec{i} + 1\vec{j} + \lambda\vec{k}$ are perpendicular, find the value of $\lambda$ .

The derivative of $\ln(\sin(2x))$ with respect to $x$ is:

Evaluate the limit: $\lim_{x \to 0} \frac{\tan(7x)}{x}$ for Vector Algebra.

The coordinates of the focus of the parabola $y^2 = 32x$ are:

The vector projection of $\vec{a} = \vec{i} + \vec{j}$ on $\vec{b} = \vec{i} - \vec{j}$ is: