Physics

Physics

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. a. (i) Define vector addition in the context of physical quantities. b. (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. c. (iii) Give a qualitative explanation for why both constructions in part (ii) lead to exactly the same resultant vector.
Intuitive explanation

Vector addition is about combining displacements, and the key is translating the physical magnitudes onto paper using your scale. Here, you'll draw P⃗\vec P and Q⃗\vec Q as 4 cm and 3 cm line segments at a 60° angle from a common point, then use the parallelogram (or triangle) method to find their resultant. The scale lets you measure the final vector's length and angle directly from your diagram.

Intuitive explanation

Vector addition is about combining displacements, and the key is translating the physical magnitudes onto paper using your scale. Here, you'll draw P⃗\vec P and Q⃗\vec Q as 4 cm and 3 cm line segments at a 60° angle from a common point, then use the parallelogram (or triangle) method to find their resultant. The scale lets you measure the final vector's length and angle directly from your diagram.

Browse the problem library