ABCD is a parallelogram. If $\overrightarrow{\mathrm{AB}}=\vec{a}, \overrightarrow{\mathrm{BC}}=\vec{b}$, then what is $\overrightarrow{\mathrm{BD}}$ equal to?

• A

  $\vec{a}+\vec{b}$
• B

  $\vec{a}-\vec{b}$
• C

  $-\vec{a}-\vec{b}$
• Correct answer
  D

  $-\vec{a}+\vec{b}$

Solution

$\overrightarrow{\mathrm{BC}}=\overrightarrow{\mathrm{AD}}$ $\overrightarrow{\mathrm{AB}}+\overrightarrow{\mathrm{BD}}=\overrightarrow{\mathrm{AD}}$ $\therefore \quad \overrightarrow{\mathrm{BD}}=\overrightarrow{\mathrm{AD}}-\overrightarrow{\mathrm{AB}}$ $\Rightarrow \quad \bar{b}-\bar{a}$.

Hence, the correct answer is option: 'D'.