Motion in a Plane | Class 11 Physics Notes
By ConceptScroll Team · Published on 17 July 2026 · 3 min read
Motion in a Plane – this guide gives you a concise, exam-ready overview of Motion in a Plane from Class 11 Physics, written by ConceptScroll editors and reviewed against the latest NCERT textbook.
3.4 Addition and subtraction of vectors — graphical method
Vectors obey the triangle law and parallelogram law of addition. The graphical method of vector addition involves arranging vectors head-to-tail or using the parallelogram formed by vectors.
In the head-to-tail method, vector B is placed so its tail coincides with the head of vector A. The resultant vector R is drawn from the tail of A to the head of B. This method is also called the triangle method since the vectors form three sides of a triangle.
Vector addition is commutative: A + B = B + A, as verified by reversing the order of addition graphically.
It is also associative: (A + B) + C = A + (B + C), meaning the grouping of vectors does not affect the resultant.
The null vector (zero vector) results from adding two equal and opposite vectors, having zero magnitude and no direction.
Subtraction of vectors is defined as adding the negative of a vector: A - B = A + (-B).
The parallelogram method involves placing vectors A and B with their tails at the same point, constructing a parallelogram with these vectors as adjacent sides, and drawing the diagonal from the common tail to find the resultant.
These graphical methods provide intuitive visualization of vector addition and subtraction.
📊 Diagram: Fig. 3.4 (a) Vectors A and B; (b) Vectors A and B added graphically; (c) Vectors B and A added graphically; (d) Illustrating the associative law of vector addition; Fig. 3.5 (a) Two vectors A and B, -B is also shown; (b) Subtracting vector B from vector A; Fig. 3.6 (a) Two vectors A and B with tails at common origin; (b) Sum A + B using parallelogram method; (c) Parallelogram method equivalent to triangle method; Fig. 3.7 Velocity vectors of rain and wind and resultant vector.
🧪 Activity: Activity: Graphically add two vectors using head-to-tail and parallelogram methods to verify commutative and associative properties.
🔗 Connection: This section prepares for the next topic on resolution of vectors into components along specified directions.
Frequently asked questions
A car containing explosives goes over a ramp of 45º angle and initial velocity of 20 m/sec. After 2 seconds, explosion occurs. What can be said about the trajectory of the centre of mass of the car after explosion occurs as compared to trajectory of the car without explosion.
No change in the horizontal range
A body consisting of four equal masses is subjected to pure rotational motion in space at a constant angular velocity. Each mass is released at 0º , 45º, 90º and 135º. Which of the following statement is true with respect to the centre of mass of the body after release of all four masses -
Centre of mass will be stationary and away from the centre of rotation.
3.1 State, for each of the following physical quantities, if it is a scalar or a vector: volume, mass, speed, acceleration, density, number of moles, velocity, angular frequency, displacement, angular velocity.
Volume - Scalar (has magnitude only) Mass - Scalar Speed - Scalar Acceleration - Vector (has magnitude and direction) Density - Scalar Number of moles - Scalar Velocity - Vector Angular frequency - Scalar Displacement - Vector Angular velocity - Vector
3.2 Pick out the two scalar quantities in the following list: force, angular momentum, work, current, linear momentum, electric field, average velocity, magnetic moment, relative velocity.
The two scalar quantities are: work and current. Explanation: Work is scalar because it has magnitude only. Current is scalar as it is a measure of charge flow rate without direction. Force, angular momentum, linear momentum, electric field, average velocity, magnetic moment, and relative velocity are vectors.
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