Mechanics · Quick Reference

Scalars & Vectors Cheat Sheet

Mechanics · Lesson 3/19

In one line: scalars describe just 'how much,' while vectors also describe 'which way' — this distinction matters enormously in physics, where direction often changes everything.

Key Ideas

1Scalar Quantity. A quantity fully described by magnitude alone, with no direction, like mass, temperature, or time.

2Vector Quantity. A quantity described by both magnitude AND direction, like displacement, velocity, or force.

3Vector Notation. Often written as an arrow over a symbol, or in component form like (x,y) for a 2D vector.

4Vector Addition. Vectors add component-wise: (a,b) + (c,d) = (a+c, b+d); graphically, vectors add 'tip to tail'.

5Magnitude of a Vector. For a vector (x,y), magnitude = sqrt(x^2+y^2), using the Pythagorean theorem.

Worked Examples

Is 'speed' a scalar or vector quantity?

Scalar

Is 'velocity' a scalar or vector quantity?

Vector

Find the magnitude of the displacement vector (3,4) meters.

5 meters

Formulas

Magnitude of (x,y) = sqrt(x^2+y^2)

(a,b) + (c,d) = (a+c, b+d)

Practice Yourself

Is 'mass' a scalar or vector?

Scalar

Is 'force' a scalar or vector?

Vector

Is 'temperature' a scalar or vector?

Scalar