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.
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.
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.