Vector Resolution - MCQ Test

🧮 Vector Resolution Test

Master the concepts of vector resolution in 2D and 3D space

📋 Test Instructions

Topic: Resolution of Vector in Two and Three Dimensional

Questions: 10 MCQs (1 mark each)

Time: No time limit - Focus on understanding

Evaluation: 8+ marks = Good | 5-7 marks = Average | <5 marks = Needs Improvement

1. What does vector resolution mean?

Finding the magnitude of a vector
Breaking a vector into its component vectors along specified directions
Adding two or more vectors together
Finding the direction of a vector

2. In two-dimensional vector resolution, how many components does a vector have?

One component
Two components
Three components
Four components

3. What are the standard unit vectors in three-dimensional space?

î and ĵ only
î, ĵ, and k̂
x̂ and ŷ only
r̂ and θ̂

4. The components of a vector are always:

Parallel to the original vector
Perpendicular to each other
Equal in magnitude
In the same direction as the original vector

5. Which statement is true about vector resolution?

Resolution changes the magnitude of the original vector
The resolved components when added vectorially give back the original vector
Resolution is only possible in 2D space
Components are always larger than the original vector

6. In 3D space, what information is needed to completely resolve a vector?

Only the magnitude
Magnitude and one angle
Magnitude and direction (or three direction cosines)
Only the direction

7. What is the relationship between a vector and its components?

The vector is the scalar sum of its components
The vector is the vector sum of its components
Components are independent of the original vector
The vector is always smaller than its components

8. Which property is true for orthogonal components of a vector?

They are parallel to each other
They are perpendicular to each other
They have the same magnitude
They point in opposite directions

9. The process of vector resolution is the reverse of:

Vector multiplication
Vector addition (composition)
Vector subtraction
Vector division

10. Why is vector resolution important in physics?

It makes calculations more complex
It allows analysis of vector quantities along specific directions of interest
It changes the physical meaning of vectors
It is only used for mathematical convenience

🎯 Test Results

0/10

📚 Solutions & Explanations

Question 1: Correct Answer - B

Explanation: Vector resolution is the process of breaking a single vector into its component vectors along specified directions (usually perpendicular axes). This is fundamental to analyzing vector quantities in different coordinate systems.

Question 2: Correct Answer - B

Explanation: In two-dimensional space, any vector can be resolved into exactly two components, typically along the x-axis and y-axis (horizontal and vertical directions).

Question 3: Correct Answer - B

Explanation: The standard unit vectors in three-dimensional Cartesian coordinate system are î (x-direction), ĵ (y-direction), and k̂ (z-direction). These form an orthonormal basis.

Question 4: Correct Answer - B

Explanation: When resolving a vector into orthogonal components, these components are always perpendicular to each other. This orthogonality is what makes the resolution unique and mathematically convenient.

Question 5: Correct Answer - B

Explanation: The fundamental principle of vector resolution states that when the resolved components are added vectorially (using vector addition rules), they exactly reproduce the original vector.

Question 6: Correct Answer - C

Explanation: To completely resolve a vector in 3D space, you need both its magnitude and complete directional information. This can be provided by direction cosines or angles with all three coordinate axes.

Question 7: Correct Answer - B

Explanation: A vector is the vector sum (not scalar sum) of its components. This means both magnitude and direction are preserved when components are added using vector addition rules.

Question 8: Correct Answer - B

Explanation: Orthogonal components are, by definition, perpendicular to each other. This perpendicularity ensures that each component captures the vector's influence in independent directions.

Question 9: Correct Answer - B

Explanation: Vector resolution is the reverse process of vector composition (addition). While composition combines components to form a resultant vector, resolution breaks a vector into its components.

Question 10: Correct Answer - B

Explanation: Vector resolution is crucial in physics because it allows us to analyze how vector quantities (like force, velocity, acceleration) act along specific directions of interest, making complex problems manageable.