Q. 3 - Calculus

Question

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

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

Step-by-Step Solution

Answer

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

Step 1: Given

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

Step 2: Simplify

From the law of  vector addition,

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

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