Two displacement vectors ( P ) and ( Q ) are represented from a common point (O )…

PHYSICS · Multi-part · CBSE · Physics · Motion in a Plane · Motion in a Plane

Problem

Two displacement vectors P⃗\vec P and Q⃗\vec Q are represented from a common point OO such that ∣P⃗∣=4 m|\vec P| = 4\,\text{m}, ∣Q⃗∣=3 m|\vec Q| = 3\,\text{m} and the angle between them is 60∘60^{\circ}. A student chooses the scale 1 cm≡1 m1\,\text{cm} \equiv 1\,\text{m} to work on plain paper. (i) Define vector addition in the context of physical quantities. (ii) Describe, with neat labelled sketches, two different graphical constructions by which the student can obtain the resultant of P⃗\vec P and Q⃗\vec Q. No actual measurement of the resultant is required. (iii) Give a qualitative explanation for why both constructions in part (ii) lead to exactly the same resultant vector.

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