Topic 4: Resolution of Vectors

Q1. Resolution of a vector means:
A) Adding vectors
B) Subtracting vectors
C) Splitting a vector into components
D) Changing magnitude of vector

Answer: C


Q2. A vector is generally resolved along:
A) Any direction
B) Parallel directions
C) x and y axes
D) Circular path

Answer: C


Q3. If a vector R makes an angle θ with x-axis, its x-component is:
A) R sinθ
B) R tanθ
C) R cosθ
D) R / cosθ

Answer: C


Q4. The y-component of a vector R is:
A) R cosθ
B) R sinθ
C) R tanθ
D) R cotθ

Answer: B


Q5. Components of a vector are always:
A) Parallel
B) Opposite
C) Perpendicular
D) Equal

Answer: C


Q6. Magnitude of resultant from components R<sub>x</sub> and R<sub>y</sub> is:
A) R<sub>x</sub> + R<sub>y</sub>
B) R<sub>x</sub> − R<sub>y</sub>
C) √(R<sub>x</sub><sup>2</sup> + R<sub>y</sub><sup>2</sup>)
D) R<sub>x</sub> × R<sub>y</sub>

Answer: C


Q7. Direction of a vector is given by:
A) sinθ = R<sub>y</sub>/R
B) cosθ = R<sub>x</sub>/R
C) tanθ = R<sub>y</sub>/R<sub>x</sub>
D) tanθ = R<sub>x</sub>/R<sub>y</sub>

Answer: C


Q8. Resolution of vectors is most useful in:
A) One-dimensional motion
B) Two-dimensional motion
C) Circular motion only
D) Rest condition

Answer: B

Chapter 4: Motion in a Plane

Topic 4: Resolution of Vectors – Quick Revision

1. Resolution

Process of splitting a vector into perpendicular components.

2. Components

R_x = R cosθ
R_y = R sinθ

3. Resultant from Components

R = √(R_x² + R_y²)

4. Direction

tanθ = R_y / R_x

5. Key Points

• Components are perpendicular
• Used in projectile motion

Exam Focus (MHT-CET)

MCQs and numericals are asked directly on vector components and angle calculation.