Question

Trace the vectors in FIGURE EX3.1 onto your paper. Then find.

(a)$\overrightarrow{A}+\overrightarrow{B}$and (b)$\overrightarrow{A}-\overrightarrow{B}.$

Short answer

(a) $\overrightarrow{A}+\overrightarrow{B}=\left(A_1+B_1,A_2+B_2\right).$

(b)$\overrightarrow{A}-\overrightarrow{B}=\left(A_1-B_1,A_2-B_2\right).$

Step-by-step solution

Part (a) Step 1. Given information

The given figure is, dds

We need to trace the figure and determine$\overrightarrow{A}+\overrightarrow{B}.$

Step 2. Calculationk

By vector addition,

$\overrightarrow{A}+\overrightarrow{B}=\left(A_1+B_1,A_2+B_2\right).$

Part (b) Step 1. Given information

The given figure is,

We need to trace the figure and determine$\overrightarrow{A}-\overrightarrow{B}.$

Step 2. Calculation

By vector subtraction,

$\overrightarrow{A}-\overrightarrow{B}=\overrightarrow{A}+\left(-\overrightarrow{B}\right).$

$=\left(A_1-B_1,A_2-B_2\right).$