Question

How do you subtract two vectors algebraically? Geometrically

Short answer

$$\begin{gathered} u=x_{1}i+y_{1}j\mathrm{and}v=x_{2}i+y_{2}j \\ \overrightarrow{u}-\overrightarrow{v}=\left(x_1-x_2\right)i+(y_1-y_2) \end{gathered}$$

Step-by-step solution

Subtract two vectors algebraically 

Let two vectors are,

$$\begin{gathered} u=x_{1}i+y_{1}j\mathrm{and}v=x_{2}i+y_{2}j \\ \overrightarrow{u}-\overrightarrow{v}=\left(x_1-x_2\right)i+(y_1-y_2) \end{gathered}$$

Example:

role="math" localid="1663308079530" $$\begin{gathered} \overrightarrow{u}=3i+8j\mathrm{and}\overrightarrow{v}=2i-4j \\ \overrightarrow{u}-\overrightarrow{v}=\left(3i-2i\right)+\left(8j+4j\right) \\ =i+12j \end{gathered}$$

Subtract two vectors geometrically 

To subtract two vectors geometrically we position their initial points together, as we see in the right-hand figure. The vector $u-v$extends from the terminal point of v to the terminal point of u.

Example:

localid="1663308270938" $$\begin{gathered} \overrightarrow{u}=3i+8j\mathrm{and}\overrightarrow{v}=2i-4j \\ \overrightarrow{u}-\overrightarrow{v}=\left(3i-2i\right)+\left(8j+4j\right) \\ =i+12j \end{gathered}$$