What Is a Vector?

A vector is a quantity that has both magnitude (size) and direction.

Examples:

• Velocity (speed and direction)

• Force

• Displacement

A scalar has only size, not direction.
Example: temperature, distance, mass

Vectors are often written using components:
v = <x, y>

Vector Algebra

Explanation

Vector algebra involves adding, subtracting, and scaling vectors.

Vector Addition:
Add corresponding components.
<2, 3> + <4, 1> = <6, 4>

Vector Subtraction:
Subtract corresponding components.
<5, 7> − <2, 4> = <3, 3>

Scalar Multiplication:
Multiply each component by a number.
3<1, 2> = <3, 6>

Vector algebra is used in physics, engineering, and computer graphics.