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Physics · Class 9 · Chapter 5: Vectors

8 min

Key points

Vector — A physical quantity which has both magnitude and direction is called a vector
Scalar — A physical quantity which has only magnitude but no direction is called a scalar
Vectors are represented by arrows where length shows magnitude and arrowhead shows direction
Addition of vectors follows triangle law and parallelogram law
Resultant vector — The single vector which produces the same effect as produced by a number of vectors jointly
Component of vector — The perpendicular projection of a vector along any direction is called component
Unit vector — A vector of unit magnitude in any direction is called unit vector
Vectors can be added graphically by head-to-tail method or parallelogram method
Analytical method uses trigonometry to find resultant using Pythagorean theorem

Definitions

Vector: A physical quantity which has both magnitude and direction is called a vector
Scalar: A physical quantity which has only magnitude but no direction is called a scalar
Resultant Vector: The single vector which produces the same effect as produced by a number of vectors jointly is called resultant vector
Unit Vector: A vector of unit magnitude in any direction is called unit vector
Component of Vector: The perpendicular projection of a vector along any direction is called component of vector

Worked example

Define vector quantity and find the resultant of two forces 3N and 4N acting at right angles to each other. (5 marks)

Vector quantity is a physical quantity which has both magnitude and direction. Examples: force, velocity, displacement. Resultant = 5N at angle θ = tan⁻¹(4/3) = 53.13° with 3N force.

Common mistakes

Students confuse scalar and vector - remember vectors need both magnitude AND direction
Forgetting to draw arrowheads on vector diagrams
Using simple addition for vectors instead of vector addition laws
Not converting angle to correct quadrant in analytical method
Mixing up sine and cosine in component calculations

Quick recap

Vector quantities have both magnitude and direction (force, velocity, displacement) while scalar quantities have only magnitude (distance, speed, mass). Vectors can be added using triangle law, parallelogram law, or rectangular components method. Always remember to include direction in final answers and use proper vector notation with arrows in diagrams.

Generated by AI from Sindh Textbook Board material; review state: ai_unreviewed. MCQs, past-paper references and examiner notes are held back until a teacher has checked them.