Lesson 2 of 10 · 6 min
Multiplying a vector by a number
NCERT §3.3
The ball runs away past Meera. She chases at 5 m/s east; Arjun, closer and quicker, sprints at twice her velocity; after the ball is thrown in, Meera jogs back at the same speed but heading west. Every one of these is her 5 m/s, stretched or flipped.
The lesson in notes
In short
Multiplying a vector A by a positive number λ gives λA: same direction, magnitude λ|A|. A 5 m/s velocity east doubled is 10 m/s east.
Multiplying by a negative number reverses the direction: −1 × (5 m/s east) is 5 m/s west, and −1.5A points opposite to A with 1.5 times its length.
If λ carries a dimension, the product has a new dimension: a constant velocity (m/s) times a time (s) gives a displacement (m).
−A has the same magnitude as A and the opposite direction; this is what makes subtraction possible.