same direction. **

Figure . (a) shows two equal vectors A and B . We can easily check their equality. Shift B parallel to itself until its tail Q coincides with that of A , i.e.

Q coincides with O. Then, since their tips S and P also coincide, the two vectors are said to be equal. In general, equality is indicated * Addition and subtraction of scalars make sense only for quantities with same units. However, you can multiply and divide scalars of different units.

** In our study, vectors do not have fixed locations. So displacing a vector parallel to itself leaves the vector unchanged. Such vectors are called f ree vectors. However, in some physical applications, location or line of application of a vector is important.

Such vectors are called localised vectors. as A = B . Note that in Fig. .

(b), vectors A ′ and B ′ have the same magnitude but they are not equal because they have different directions. Even if we shift B ′ parallel to itself so that its tail Q ′ coincides with the tail O ′ of A ′ , the tip S ′ of B ′ does not coincide with the tip P ′ of A ′ .