Question

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

role="math" localid="1663231338982" $\overrightarrow{AB}+\overrightarrow{BC}$

Short answer

$\overrightarrow{AB}+\overrightarrow{BC}=\overrightarrow{AC}$

Step-by-step solution

Given

$\overrightarrow{AB}+\overrightarrow{BC}$

Simplify

From the law of vector addition,

$\overrightarrow{AB}+\overrightarrow{BC}=\overrightarrow{AC}$

Thus,$\overrightarrow{AB}+\overrightarrow{BC}$is represented by vector$\overrightarrow{AC}$.