My Learning Cart
?
Categories
Account

Vector & 3D Geometry

Download Q&A
Q. If the vectors A = (x, 2, 3) and B = (4, y, 6) are orthogonal, what is the value of y?
  • A. 2
  • B. 3
  • C. 4
  • D. 5
Q. If u = (1, 2) and v = (3, 4), what is the dot product u · v?
  • A. 10
  • B. 11
  • C. 12
  • D. 7
Q. If u = (1, 2) and v = (3, 4), what is u + v?
  • A. (4, 6)
  • B. (2, 3)
  • C. (1, 2)
  • D. (3, 4)
Q. If u = (1, 2, 3) and v = (4, 5, 6), what is the dot product u · v?
  • A. 32
  • B. 27
  • C. 26
  • D. 30
Q. If u = (2, 3, 1) and v = (1, 0, -1), find the dot product u · v.
  • A. 5
  • B. 2
  • C. 1
  • D. 0
Q. If vector A = (1, 2, 3) and vector B = (4, 5, 6), what is A + B?
  • A. (5, 7, 9)
  • B. (4, 5, 6)
  • C. (1, 2, 3)
  • D. (0, 0, 0)
Q. If vector A = (1, 2, 3) and vector B = (4, 5, 6), what is the angle between them?
  • A. 0 degrees
  • B. 30 degrees
  • C. 60 degrees
  • D. 90 degrees
Q. If vector A = (1, 2, 3) and vector B = (4, 5, 6), what is the vector A - B?
  • A. (-3, -3, -3)
  • B. (3, 3, 3)
  • C. (5, 7, 9)
  • D. (0, 0, 0)
Q. If vector A = (2, 2, 2) and vector B = (1, 1, 1), what is the scalar triple product A . (B × A)?
  • A. 0
  • B. 1
  • C. 2
  • D. 3
Q. If vector A = (3, -2, 1) and vector B = (1, 4, -3), what is the cross product A × B?
  • A. (-5, -10, 14)
  • B. (5, 10, -14)
  • C. (10, 14, 5)
  • D. (14, -5, 10)
Q. If vectors A = (x, 2, 3) and B = (1, y, 4) are perpendicular, what is the value of x + y?
  • A. 1
  • B. 2
  • C. 3
  • D. 4
Q. If vectors A = 3i + 4j and B = 2i - j, what is the scalar product A · B?
  • A. -1
  • B. 2
  • C. 10
  • D. 11
Q. The scalar product of two unit vectors is 0. What can be said about these vectors?
  • A. They are parallel
  • B. They are orthogonal
  • C. They are collinear
  • D. They are equal
Q. The scalar product of vectors A = (a, b, c) and B = (1, 2, 3) is 14. If a = 2, find b and c.
  • A. 3, 4
  • B. 4, 3
  • C. 5, 2
  • D. 2, 5
Q. The scalar product of vectors A = (a, b, c) and B = (1, 2, 3) is 14. If a = 2, what is the value of b + c?
  • A. 4
  • B. 5
  • C. 6
  • D. 7
Q. What is the angle between the vectors (1, 0) and (0, 1)?
  • A. 0 degrees
  • B. 90 degrees
  • C. 45 degrees
  • D. 180 degrees
Q. What is the angle between the vectors (1, 2, 2) and (2, 1, 2)?
  • A. 90 degrees
  • B. 60 degrees
  • C. 45 degrees
  • D. 30 degrees
Q. What is the angle between the vectors a = (1, 2, 2) and b = (2, 0, 2)?
  • A. 0 degrees
  • B. 45 degrees
  • C. 90 degrees
  • D. 60 degrees
Q. What is the angle between the vectors u = (1, 0) and v = (0, 1)?
  • A. 0 degrees
  • B. 90 degrees
  • C. 45 degrees
  • D. 180 degrees
Q. What is the angle between vectors A = (1, 0, 0) and B = (0, 1, 0)?
  • A. 0 degrees
  • B. 45 degrees
  • C. 90 degrees
  • D. 180 degrees
Q. What is the cross product of the vectors (1, 0, 0) and (0, 1, 0)?
  • A. (0, 0, 1)
  • B. (1, 1, 0)
  • C. (0, 0, 0)
  • D. (1, 0, 0)
Q. What is the cross product of the vectors (1, 2, 3) and (4, 5, 6)?
  • A. (-3, 6, -3)
  • B. (-3, 6, 3)
  • C. (3, -6, 3)
  • D. (3, 6, -3)
Q. What is the cross product of u = (1, 2, 3) and v = (4, 5, 6)?
  • A. (-3, 6, -3)
  • B. (0, 0, 0)
  • C. (3, -6, 3)
  • D. (1, 2, 3)
Q. What is the cross product of vectors (1, 2, 3) and (4, 5, 6)?
  • A. (-3, 6, -3)
  • B. (0, 0, 0)
  • C. (3, -6, 3)
  • D. (1, 2, 3)
Q. What is the cross product of vectors A = (1, 2, 3) and B = (4, 5, 6)?
  • A. (-3, 6, -3)
  • B. (0, 0, 0)
  • C. (3, -6, 3)
  • D. (1, -2, 1)
Q. What is the distance between the points P(1, 2, 3) and Q(4, 5, 6)?
  • A. 3√3
  • B. 3√2
  • C. 3
  • D. √3
Q. What is the dot product of vectors (1, 2) and (3, 4)?
  • A. 11
  • B. 10
  • C. 12
  • D. 7
Q. What is the dot product of vectors A = (2, 3, 4) and B = (1, 0, -1)?
  • A. -2
  • B. 5
  • C. 10
  • D. 11
Q. What is the equation of the line passing through the points (1, 2, 3) and (4, 5, 6)?
  • A. x = 1 + 3t, y = 2 + 3t, z = 3 + 3t
  • B. x = 1 + t, y = 2 + t, z = 3 + t
  • C. x = 1 + t, y = 2 + 2t, z = 3 + 3t
  • D. x = 1 + 3t, y = 2 + 2t, z = 3 + t
Q. What is the magnitude of the vector (2, -3, 6)?
  • A. 7
  • B. 9
  • C. 8
  • D. 5
Showing 151 to 180 of 210 (7 Pages)

Vector & 3D Geometry MCQ & Objective Questions

Understanding Vector & 3D Geometry is crucial for students preparing for various school and competitive exams. This topic not only enhances spatial reasoning but also forms the backbone of many important concepts in mathematics and physics. Practicing MCQs and objective questions in this area can significantly improve your exam scores and boost your confidence. Engaging with practice questions helps solidify your grasp of key concepts and prepares you for tackling important questions effectively.

What You Will Practise Here

  • Basics of vectors: definitions, types, and operations
  • Vector addition and subtraction: graphical and algebraic methods
  • Dot product and cross product: properties and applications
  • Equations of lines and planes in 3D space
  • Distance between points, lines, and planes
  • Applications of vectors in physics: force, velocity, and acceleration
  • Common theorems and formulas related to 3D geometry

Exam Relevance

Vector & 3D Geometry is a significant topic in CBSE, State Boards, NEET, and JEE exams. Students can expect questions that assess their understanding of vector operations, geometric interpretations, and problem-solving skills. Common question patterns include multiple-choice questions that require students to apply concepts to real-world scenarios, as well as numerical problems that test their computational abilities.

Common Mistakes Students Make

  • Confusing the dot product and cross product, leading to incorrect applications.
  • Misinterpreting the geometric representation of vectors, especially in 3D space.
  • Overlooking the significance of direction in vector addition and subtraction.
  • Failing to apply the correct formulas for distance calculations between geometric entities.

FAQs

Question: What are the key formulas I should remember for Vector & 3D Geometry?
Answer: Important formulas include the dot product formula, cross product formula, and distance formulas between points, lines, and planes.

Question: How can I improve my understanding of Vector & 3D Geometry concepts?
Answer: Regular practice of MCQs and solving objective questions will help reinforce your understanding and application of these concepts.

Start your journey towards mastering Vector & 3D Geometry today! Solve practice MCQs to test your understanding and enhance your exam preparation. Your success is just a question away!

Soulshift Feedback ×

On a scale of 0–10, how likely are you to recommend The Soulshift Academy?

Not likely Very likely
Home Practice Performance eBooks