Position and Displacement Vectors – Easy NEET Notes
- Dr.Sanjaykumar pawar
1. Position of an Object
- To describe the position of an object in a plane, we first choose a fixed point.
- This fixed point is called the origin (O).
- Origin is the reference point for all measurements.
2. Position Vector
- Let an object be at point P at time t.
- We join origin O to point P using a straight line.
- This line represents the position vector.
3. Representation of Position Vector
- The line OP is called the position vector.
- It is written as:
- An arrow is placed on top or at the end to show direction.
- Position vector shows:
- Distance from origin
- Direction from origin
4. Change of Position with Time
- At a later time t′, the object moves to point P′.
- So the position of the object changes with time.
- This means position vector also changes.
5. Displacement Vector
- Displacement is the change in position of an object.
- It is represented by a straight line from initial position to final position.
6. Definition of Displacement Vector
- If an object moves from point P to Q, then:
- The displacement vector is PQ
- It is a vector quantity.
- It has both:
7. Important Property of Displacement
- Displacement depends only on:
- Initial position
- Final position
- It does NOT depend on the path taken.
8. Path Independence
- An object may take different paths to reach the same point.
- Example:
- P → A → B → C → Q
- P → D → Q
- P → B → E → F → Q
- In all cases:
- Displacement remains the same → PQ
9. Key Concept
- Displacement is always the shortest straight line between two points.
- It is independent of the route taken.
10. Distance vs Displacement (Important NEET Point)
- Distance = actual path length travelled.
- Displacement = straight line between initial and final position.
11. Magnitude Relation
- Magnitude of displacement is:
- Always less than or equal to distance
- Cases:
- If motion is straight line → distance = displacement
- If motion is curved → distance > displacement
12. Final Important Conclusion
- Displacement gives only change in position.
- It does not depend on how the object moved.
- This idea is important in both straight line and plane motion.
Quick Revision Points
- Position vector = origin to point (OP = r)
- Displacement vector = initial to final position (PQ)
- Displacement is path independent
- Distance ≥ displacement always
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| Position and Displacement Vectors explained with origin, paths, and straight-line displacement for easy NEET understanding. |
Class 11 Physics (CBSE/NEET Level)
Position and Displacement Vectors – Question Bank
1. MCQs (Multiple Choice Questions)
Q1. Position vector is:
A) From object to origin
B) From origin to object
C) Between two objects
D) Always zero
Answer: B) From origin to object
Q2. Displacement depends on:
A) Path taken
B) Initial and final position
C) Speed
D) Time only
Answer: B) Initial and final position
Q3. Displacement is:
A) Scalar
B) Vector
C) Always zero
D) Always equal to distance
Answer: B) Vector
Q4. Which is true?
A) Distance ≤ Displacement
B) Distance ≥ Displacement
C) Distance = 0 always
D) Displacement is path dependent
Answer: B) Distance ≥ Displacement
Q5. Position vector is represented as:
A) PQ
B) OP = r
C) PQ = 0
D) OQ only
Answer: B) OP = r
2. Very Short Answer Questions
Q1. What is position vector?
Answer:
It is the vector from origin to the position of an object.
Q2. What is displacement?
Answer:
Change in position of an object from initial to final point.
Q3. Is displacement scalar or vector?
Answer:
Vector.
Q4. Does displacement depend on path?
Answer:
No.
Q5. What is origin?
Answer:
A fixed reference point used to describe position.
3. Short Answer Questions
Q1. Differentiate between distance and displacement.
Answer:
| Distance |
Displacement |
| Scalar |
Vector |
| Path dependent |
Path independent |
| Always positive |
Can be positive, negative, or zero |
| Actual path length |
Shortest straight line |
Q2. Why is displacement a vector quantity?
Answer:
Because it has both magnitude and direction from initial to final position.
Q3. Explain position vector.
Answer:
Position vector is a vector drawn from origin to the position of an object. It gives both distance and direction of object from origin.
4. Long Answer Questions
Q1. Explain position vector and displacement vector with diagram description.
Answer:
To describe motion in a plane, a fixed point called origin is chosen. The position of an object at time t is given by a vector from origin to the object, called position vector OP = r. When the object changes position from P to Q, the vector joining initial to final position is called displacement vector PQ. Displacement depends only on initial and final positions, not on path taken.
Q2. Explain why displacement is independent of path.
Answer:
Displacement depends only on initial and final positions. Even if an object moves through different paths like PABCQ or PDQ, the straight line joining P and Q remains same. Therefore displacement is path independent.
5. Assertion and Reason
Q1.
Assertion (A): Displacement is a vector quantity.
Reason (R): It has only magnitude.
Answer: C
(A is true, R is false)
Q2.
Assertion (A): Distance is always greater than or equal to displacement.
Reason (R): Distance is actual path length.
Answer: A
(Both true and R correctly explains A)
Q3.
Assertion (A): Displacement depends on path.
Reason (R): It is a vector quantity.
Answer: D
(A is false, R is true)
6. Fill in the Blanks
- Position vector is written as OP = r.
- Displacement is the change in position.
- Displacement is a vector quantity.
- Distance is always greater than or equal to displacement.
- Position vector starts from origin.
7. Case Study Questions
Case Study:
A student moves from point P to Q following three different paths: PABCQ, PDQ, and PBEFQ. The initial and final positions are same in all cases.
Q1. What remains same in all paths?
Answer: Displacement
Q2. What changes in different paths?
Answer: Distance
Q3. Why is displacement same?
Answer: Because it depends only on initial and final positions.
Q4. Is displacement scalar or vector?
Answer: Vector
8. Statement Questions (True/False)
Q1. Position vector starts from origin.
Answer: True
Q2. Displacement depends on path.
Answer: False
Q3. Distance is a vector quantity.
Answer: False
Q4. Displacement can be zero.
Answer: True
9. Match the Columns
| Column A |
Column B |
| 1. Position vector |
A. Path independent |
| 2. Displacement |
B. OP = r |
| 3. Distance |
C. Scalar |
| 4. Vector |
D. Magnitude + direction |
Answers:
1 → B
2 → A
3 → C
4 → D
10. Extra Important Questions
Q1. Can displacement be zero?
Answer: Yes, if initial and final positions are same.
Q2. What is shortest distance in motion?
Answer: Displacement.
Q3. Why is position vector important?
Answer: It gives location of object in space relative to origin.
Suggested Internal Links
Scalars and Vectors Notes
Motion in a Straight Line Class 11
Motion in a Plane Complete Chapter
Distance vs Displacement Explained
Vector Addition Methods
Projectile Motion Notes
Circular Motion Basics
Kinematics Formulas Sheet
NEET Physics Important Questions
CBSE Class 11 Physics MCQs
POSITION AND DISPLACEMENT VECTORS
│
├── 1. Position of Object
│ │
│ ├── Need reference point
│ │ └── Origin (O)
│ │
│ ├── Object position at time t
│ │ └── Point P
│ │
│ └── Position description uses vector
│
├── 2. Position Vector
│ │
│ ├── Defined as
│ │ └── Vector from origin to position
│ │
│ ├── Representation
│ │ └── OP = r
│ │
│ └── Meaning
│ ├── Magnitude = distance from origin
│ └── Direction = from origin to object
│
├── 3. Change in Position
│ │
│ ├── At time t → position P
│ └── At time t' → position P'
│
├── 4. Displacement Vector
│ │
│ ├── Definition
│ │ └── Change in position
│ │
│ ├── Representation
│ │ └── PQ (from initial to final position)
│ │
│ └── Nature
│ ├── Vector quantity
│ └── Has magnitude and direction
│
├── 5. Path Independence
│ │
│ ├── Displacement depends only on
│ │ ├── Initial position
│ │ └── Final position
│ │
│ ├── Does NOT depend on path
│ │ ├── PABCQ
│ │ ├── PDQ
│ │ └── PBEFQ
│ │
│ └── Same displacement for all paths
│
├── 6. Distance vs Displacement
│ │
│ ├── Distance
│ │ └── Actual path length
│ │
│ ├── Displacement
│ │ └── Straight line between two points
│ │
│ └── Relation
│ └── Distance ≥ Displacement
│
└── 7. Important Results
│
├── Straight motion → distance = displacement
├── Curved motion → distance > displacement
└── Displacement is shortest path
