Q. 9 - Calculus

Question

How do you add two vectors algebraically? Geometrically 

Step-by-Step Solution

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 1: 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:

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

Step 2: Addition of vectors geometrically

Let,

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