**Vectors**

**There are two types of quantities**

Scalar quantities require only magnitude

Examples include counted items, time
and speed

Vector quantities require magnitude and direction.

Examples include displacement,
velocity, and acceleration.

**Properties of Vectors**

Equality of vectors

Two vectors are equal if and only if
their magnitudes and their directions are the same.

Adding Vectors

Vector A can be added to Vector B to
form a Resultant Vector or Vector R

Vectors follow the commutative law of
addition

Vector A + Vector B = Vector B +
Vector A

Vectors can be added geometrically.

Use graph
paper, ruler, compass, and protractor.

Vectors can be added algebraically.

Use algebra
and trigonometry

Vectors can be added via the
parallelogram method of addition.

Negative of a vector

Vector A + (-Vector A) = 0

The negative of a vector has same
magnitude as the original vector but the opposite direction.

Subtracting Vectors

Vector B can be subtracted from
Vector A to form a Resultant vector R.

Vector A - Vector B = Vector A +
(-Vector B)

Vector subtraction is a special case
of vector addition.

Multiplying a Vector by a Scalar

Vectors can be multiplied by a scalar
quantity.

Vector A
times the scalar quantity 2 results in 2 times Vector A.

Vector Components