01 Key Concepts
Scalar Quantity
A quantity fully described by magnitude alone, with no direction, like mass, temperature, or time.
Vector Quantity
A quantity described by both magnitude AND direction, like displacement, velocity, or force.
Vector Notation
Often written as an arrow over a symbol, or in component form like (x,y) for a 2D vector.
Vector Addition
Vectors add component-wise: (a,b) + (c,d) = (a+c, b+d); graphically, vectors add 'tip to tail'.
Magnitude of a Vector
For a vector (x,y), magnitude = sqrt(x^2+y^2), using the Pythagorean theorem.
02 Key Formulas
- Magnitude of (x,y) = sqrt(x^2+y^2)
- (a,b) + (c,d) = (a+c, b+d)
03 Solved Examples
Example 1 Is 'speed' a scalar or vector quantity?
- Speed describes only how fast something moves, with no direction specified.
Answer: Scalar
Example 2 Is 'velocity' a scalar or vector quantity?
- Velocity describes both how fast AND in what direction something moves.
Answer: Vector
Example 3 Find the magnitude of the displacement vector (3,4) meters.
- Apply the formula: sqrt(3^2+4^2) = sqrt(9+16) = sqrt(25).
Answer: 5 meters
04 Practice Questions
1Is 'mass' a scalar or vector?
Scalar
2Is 'force' a scalar or vector?
Vector
3Is 'temperature' a scalar or vector?
Scalar
4Find the magnitude of the vector (6,8).
10
5Add the vectors (2,3) and (1,4).
(3,7)
📄 Scalars & Vectors — Downloadable Worksheet
10 questions with a full answer key. Grab the PDF to print, or try the interactive version in your browser.