Components of vectors

If we have two vectors in different directions on the same plane, all the vectors on the plane can be represented by these two base vectors. These are basis of the plane.

Above are the vectors i and j with a length of 1 square. Vectors a, b and c can be expressed by vectors i and j.

The components of the vectors with same basis are unique. If two vectors have the same components, it is the same vector.

Example 1:

Break vector a into components parallel to vectors b and c. The vectors i and j are perpendicular unit vectors.

We have to find n and t so that

Vectors have the same basis, so the components are unique. We get a pair of linear equations

The solution of the pair of equations is n = 2 and t = 1. Then vector a described with vectors b and c is

Turn on the subtitles if needed