Question

Four vectors each of equal magnitude are given below.

Which of the following statement is correct regarding these vectors ?

• A. $\overrightarrow{\text{A}}+\overrightarrow{\text{B}}=-(\overrightarrow{\text{C}}+\overrightarrow{\text{D}})$
• B. $\overrightarrow{\text{A}}+\overrightarrow{\text{B}}=\overrightarrow{\text{C}}-\overrightarrow{\text{D}}$
• C. $\overrightarrow{\text{A}}+\overrightarrow{\text{B}}=\overrightarrow{\text{C}}+\overrightarrow{\text{D}}$
• D. None of the above

Answer 1

The correct option is A $\overrightarrow{\text{A}}+\overrightarrow{\text{B}}=-(\overrightarrow{\text{C}}+\overrightarrow{\text{D}})$

$\overrightarrow{\text{A}}+\overrightarrow{\text{B}}$ can be shown as,


From the diagram, $\overrightarrow{\text{X}}=\overrightarrow{\text{A}}+\overrightarrow{\text{B}}$

$\overrightarrow{\text{C}}+\overrightarrow{\text{D}}$ can be shown as,


From the diagram, $\overrightarrow{\text{Y}}=\overrightarrow{\text{C}}+\overrightarrow{\text{D}}$

Comparing the figures, we can say that,

$\overrightarrow{\text{X}}=-\overrightarrow{\text{Y}}$

$\therefore \overrightarrow{\text{A}}+\overrightarrow{\text{B}}=-(\overrightarrow{\text{C}}+\overrightarrow{\text{D}})$

Hence, option $\text{(B)}$ is the correct answer.