Question

Use the figure at the right. Determine whether the given statement is true or false.

$C=D-E+F$

Short answer

The given statement is False.

Step-by-step solution

Step 1. Given Information 

We are given a statement $C=D-E+F$and we need to find if the statement is true or false.

Step 2. Proving the statement 

$D-E$implies subtraction of two vectors.

So the terminal point of the vector $D$is joined with the terminal point of the vector $E$forming vector $D-E$.

The vector role="math" localid="1646710367263" $F-E$implies subtraction of two vectors.

So the initial point of the vector $E$is joined with the initial point of the vector $F$forming vector $F-E$.

Again, the initial point of vector $C$coincides with the terminal point of vector $F$and the terminal point of vector $C$coincides with the initial point of vector $D$.

$\therefore D-E+F=-C$

Therefore, the given statement $C=D-E+F$is false.