If $\overrightarrow{\mathbf{a}}, \overrightarrow{\mathbf{b}}, \overrightarrow{\mathbf{c}}$ are three vectors such that $\overrightarrow{\mathbf{a}}=\overrightarrow{\mathbf{b}}+\overrightarrow{\mathbf{c}}$ and the angle between $\overrightarrow{\mathbf{b}}$ and $\overrightarrow{\mathbf{c}}$ is $\frac{\pi}{2}$, then:

• Correct answer
  A

  $a^2=b^2+c^2$
• B

  $b^2=c^2+a^2$
• C

  $c^2=a^2+b^2$
• D

  $2 a^2-b^2=c^2$

Solution

Given that $\overrightarrow{\mathbf{a}}=\overrightarrow{\mathbf{b}}+\overrightarrow{\mathbf{c}}$
and $\overrightarrow{\mathbf{b}} \perp \overrightarrow{\mathbf{c}}$ then $(\overrightarrow{\mathbf{a}})^2=(\overrightarrow{\mathbf{b}})^2+(\overrightarrow{\mathbf{c}})^2$ $a^2=b^2+c^2$

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