Lesson 1 of 10 · 6 min
The scalar product
NCERT § "The Scalar Product"
Kiran pulls the supply trolley with a rope at 60° to the ground. He pulls with 50 N, yet the trolley only feels part of that along the road. Which part, and how do we multiply a force by a distance when they point different ways?
The lesson in notes
In short
The scalar (dot) product of two vectors is A·B = AB cos θ, with θ the angle between them; the result is a scalar.
In components, A·B = AxBx + AyBy + AzBz; for unit vectors î·î = 1 and î·ĵ = 0.
The dot product is commutative (A·B = B·A) and distributive over addition.
A·B is positive for θ < 90°, zero for θ = 90° and negative for θ > 90°.
Geometrically, A·B is the magnitude of one vector times the projection of the other on it.
The angle between two vectors can be found from cos θ = A·B/(AB).