Question

In Exercises 3–8, let A, B, C, D, ... , Z be points in $R^3$. Simplify the given quantity.

role="math" localid="1663305327547" $\overrightarrow{AB}+\overrightarrow{BA}$

Short answer

$\overrightarrow{AB}+\overrightarrow{BA}=0$

Step-by-step solution

Given

$\overrightarrow{AB}+\overrightarrow{BA}$

Simplify

As we know, the negative sign of any vector will change the direction of any vector.

$\overrightarrow{BA}=-\overrightarrow{AB}$

$$\begin{gathered} \overrightarrow{AB}+\overrightarrow{BA}=\overrightarrow{AB}-\overrightarrow{AB} \\ =0 \end{gathered}$$