Question

If $\overrightarrow{C}=\overrightarrow{A}+\overrightarrow{B},$Can $C=0?$Can $C<0?$For each, show how or explain why not.

Short answer

The magnitude of vector$C$can be $0$but it magnitude$C$canot be less than $0.$

Step-by-step solution

Step 1. Given information

It is given that $\overrightarrow{C}=\overrightarrow{A}+\overrightarrow{B}.$We need to write can $C=0$and can $C<0.$For each we need to showhow or explain why not.

Step 2. Explanation

Length of a vector,

A vector either has length, or it has not. Its magnitude cannot be negative.

$C$can be $0$if $\overrightarrow{A}=-\overrightarrow{B},$in which case the sum$\overrightarrow{C}$is a vector of length$0.$

Step 3. Explanation

The magnitude of a vector is always positive so the magnitude of vector $\overrightarrow{C}$can't be negative.