Chapter 14.1, Problem 4OE

To determine

To explain: Whether the statement “A parallelogram $ABCD$ have the sides $\overrightarrow{2XB}=\overrightarrow{DB}$ .” is true or false.

  

Answer to Problem 4OE

The statement “A parallelogram $ABCD$ have the sides $\overrightarrow{2XB}=\overrightarrow{DB}$ .” is true.

Explanation of Solution

Given information:

The statement “A parallelogram $ABCD$ have the sides $\overrightarrow{2XB}=\overrightarrow{DB}$ .”

Consider the provided statement “A parallelogram $ABCD$ have the sides $\overrightarrow{2XB}=\overrightarrow{DB}$ .”

Parallelogram has a property that opposite sides of a parallelogram are parallel to each other.

Parallelogram has four sides and four angles, sometimes sides and angles are equal and sometimes they may different.

Each diagonal bisects each other and each diagonal divides the quadrilateral into two equal congruent triangles.

Thus the $\overrightarrow{2XB}=\overrightarrow{DB}$ ,

Here,

  $\begin{array}{c}\overrightarrow{2XB}=\overrightarrow{DB}\\ XB=DX\end{array}$

The two vectors are of the same length and face the same direction.

  $2XB=DX+XB$

Substitute $2XB\text{ for}DB$ .

So the equation by adding the vectors:

  $2XB=DB$

The diagonals are equal and bisects each other, so these are equal but in case of vector,

The two vectors are going in two directions not in same direction.

So the given expression $2XB=DB$ is true.

Thus, the statement “A parallelogram $ABCD$ have the sides $2XB=DB$ .” is true.