You actually can add vectors algebraically, but they need to be in unit vector notation first. If you have two vectors →v1 and →v2 , you can find their sum →v3 by adding their components.

Why can vectors be added algebraically?

Because vector has both magnitude and direction . magnitude can be added algebraically but direction cannot .

Can we add vectors algebraically?

To add the vectors (x₁,y₁) and (x₂,y₂), we add the corresponding components from each vector: (x₁+x₂,y₁+y₂). Here's a concrete example: the sum of (2,4) and (1,5) is (2+1,4+5), which is (3,9).