Vector Addition

We add two Vectors together by adding the corresponding components.

a+b=[a1a2]+[b1b2]=[a1+b1a2+b2]\vec{a} + \vec{b} = \begin{bmatrix} a_1 \\ a_2 \end{bmatrix} + \begin{bmatrix} b_1 \\ b_2 \end{bmatrix} = \begin{bmatrix} a_1 + b_1 \\ a_2 + b_2 \end{bmatrix}

Vector addition requires both vectors to have equal dimensions.

We can visualize Vector addition as follows:

  1. draw the 1st Vector
  2. draw the 2nd Vector starting from the tip of the 1st Vector
  3. Draw a line from the tail of the 1st Vector to the tip of the 2nd.

Vector addition visual example

3Blue1Brown (2016)


3Blue1Brown. Vectors | Chapter 1, Essence of linear algebra. August 2016. URL: