Different types of Vectors

Different types of Vectors

1. Equal vectors: Two vectors  and  are said to be equal when they have equal magnitude and same direction and represent the same physical quantity (Figure 2.12.).

a. Collinear vectors: Collinear vectors are those which act along the same line. The angle between them can be 0° or 180°.

i. Parallel Vectors: If two vectors  and  act  in the same direction along the same line or on parallel line, then the angle between them is 00 (Figure 2.13).

ii. Anti-parallel vectors: Two vectors  and  are said to be anti-parallel when they are in opposite directions along the same line or on parallel lines. Then the angle between them is 180o (Figure 2.14).

2. Unit vector: A vector divided by its magnitude is a unit vector. The unit vector for  is denoted by Aˆ (read as A cap or A hat). It has a magnitude equal to unity or one.

Thus, we can say that the unit vector specifies only the direction of the vector quantity.

3. Orthogonal unit vectors: Let iˆ , jˆ and kˆ be three unit vectors which specify the directions along positive x-axis, positive y-axis and positive z-axis respectively. These three unit vectors are directed perpendicular to each other, the angle between any two of them is 90°. iˆ , jˆ and kˆ are examples of orthogonal vectors. Two vectors which are perpendicular to each other are called orthogonal vectors as is shown in the Figure 2.15