Decomposition of a Vector
- Roy Wright
Given any (nonzero) vectors and , you can always split into the sum of two vectors and , with in the same direction as and orthogonal to . In the illustration below, you are free to drag the tips of the vectors and .
To see how you can use and to find and , think about the following:
- should be the sum of and , so .
- should be parallel to , so for some number .
- should be orthogonal to , so .