Question

How do you add 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

Addition of vectors algebraically

If two vectors $\overrightarrow{u}\mathrm{and}\overrightarrow{v}$are given,

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

Example:

$$\begin{gathered} \overrightarrow{u}=3i+8j\mathrm{and}\overrightarrow{v}=2i-4j \\ \overrightarrow{u}+\overrightarrow{v}=\left(3i+2i\right)+\left(8j-4j\right) \\ =5i+4j \end{gathered}$$

Addition of vectors geometrically

Let,

$$\begin{gathered} \overrightarrow{u}=3i+8j\mathrm{and}\overrightarrow{v}=2i-4j \\ \overrightarrow{u}+\overrightarrow{v}=\left(3i+2i\right)+\left(8j-4j\right) \\ =5i+4j \end{gathered}$$