î and ĵ (i-hat and j-hat) represent the “1” unit size on a graph. If you think about it then, a vector is actually a scalar of î and ĵ.
therefore represents 3î + 2ĵ.
That implies that the outcome of the vector can be significantly changed by changing the size of the basis vector, since it is arbitrary.
Connections
Scaling Means To Multiply A Vector
Link Explanation: The linked note explains how vectors can be multiplied to stretch them out across a graph. But, what the current note describes is how each number in a vector is also actually a scalar of the basis vectors î and ĵ, since they represent one unit on the graph.
Reference
https://www.youtube.com/watch?v=k7RM-ot2NWY&list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab&index=2