Unit Vectors

A vector is a displacement in a certain direction. The displacement can be any distance, and can take place in one, two, three or even more dimensions.

In one dimension, the direction is indicated by the sign of the vector. Plus means to the right, in the positive direction and minus means to the left in the negative direction.

For more than one dimension the vector can be given as a column, for example(two dimensions) or(three dimensions).

The length of the vectorisWe can find the unit vector in the direction ofby dividing this vector by its length, giving

is a unit vector since its length is or 1 unit of length.

Any vectorcan be written in terms of a unit vectorsince we can takethen

Unit vectors are important because they allow easy labelling of coordinate systems. The unit vector along the x – axis isand the unit vector along the y – axis isso that the vector