Learning Introductory Physics with Activities

Suppose you have two vectors \(\vec{A}\) and \(\vec{B}\text{.}\) To add the two vectors, you will place the tail of \(\vec{B}\) at the head of \(\vec{A}\text{.}\) The vector connecting the tail of \(\vec{A}\) to the head of \(\vec{B}\) is the sum \(\vec{A} + \vec{B}\text{.}\)

To subtract two vectors, you again start by placing the vectors tail-to-tail. Then, you can rewrite the vector \(\vec{C} = \vec{A} - \vec{B}\) as \(\vec{B} = \vec{A} + \vec{C}\text{.}\) Now you can use vector addition to find \(\vec{C})\text{,}\) which is the vector that must be added to \(\vec{A}\) so that the sum of \(\vec{A}\) and \(\vec{C}\) is \(\vec{B}\text{.}\)

Alternatively, you can add the negative \(\vec{A} + (-\vec{B})\text{.}\) Recall that the negative vector points in the opposite direction but has the same length.

Multiplication of a vector with a positive scalar will scale the magnitude of the vector but leave the direction unchanged. Multiplication by a negative scalar will reverse the direction in addition to scaling the vector magnitude.