Question

Trace the vectors in FIGURE EX3.2 onto your paper. Then find.

(a) $\overrightarrow{A}+\overrightarrow{B}$and (b) $\overrightarrow{A}-\overrightarrow{B}$localid="1649527132367" $\overrightarrow{A}-\overrightarrow{B}.$

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,

We need to determine,

$\overrightarrow{A}+\overrightarrow{B}.$

Step 2. Calculation

The given figure is,

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 determine,

$\overrightarrow{A}-\overrightarrow{B}.$

Step 2. Calculation

The given figure is,

By vector subtraction,

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