SCALARS AND VECTOR There are two types of physical quantities (i) Those which have only magnitude (ii) Those which have both magnitude and direction.
A physical quantity which have only magnitude is called Scalar, while physical quantity which have both magnitude and direction is called Vector. Examples of scalars are: length, area, volume, mass, work, energy, distance, speed, density etc. Examples of vectors are: displacement, velocity, acceleration, force and momentum. Vectors which have no particular directions associated with them are called free vectors. Vectors which have a particular directions associated with them may be located along a straight line or through a particular point. Consider two towns, B which is 50km from A where B is N45ᵒE of A. The vector 50km from A in the direction North 45ᵒEast can be represented by the line segment AB in this respect, a vector can be regarded as a directed line segment . The directed line segment has initial point A and a terminal point B. This is indicated by the arrow in the line segment . The vector from A to B as a directed line segment is written as .
TERMS USED IN VECTORS 1. Notations: In printed work, a vector is shown in heavy point e.g a. In written work, a vector is shown by a letter with bar underneath it. e.g a. 2. Magnitude of a Vector: The magnitude of a vector a, sometimes called the modulus or absolute value of the vector is represented by │a│. 3. The Zero Vector: The zero vector is a vector with a magnitude of zero. The zero vector has no particular direction. It is represented by 0. The zero vector is sometimes called null vector. 4. The Unit Vector: The unit vector in the direction of a vector a is the vector represented by â and is such that a = │a│ â. 5. The Negative Vector: The negative vector of a vector a is the vector which have the same magnitude as that of a but in a direction opposite that of a. The negative vector of a is written as -a. 6. Equality of Two Vectors: Two vectors a and b are said to be equal if they have the same magnitude and direction.