Question

If $\overline{A}.(\overline{B}+\overline{C})=\overline{B}.(\overline{C}+\overline{A})=\overline{C}.(\overline{A}+\overline{B})=0$ and $|\overline{A}|=3,|\overline{B}|=4$ and $|\overline{C}|=5$ then $|\overline{A}+\overline{B}+\overline{C}|=$

• A. $5$
• B. $5\sqrt{2}$
• C. $5/\sqrt{2}$
• D. $\sqrt{2}$

Answer 1

The correct option is B $5\sqrt{2}$

Consider the problem

$|\overrightarrow{A}+\overrightarrow{B}+\overrightarrow{C}{|}^2=(\overrightarrow{A}+\overrightarrow{B}+\overrightarrow{C}).(\overrightarrow{A}+\overrightarrow{b}+\overrightarrow{C})$

$=\overrightarrow{A}.\overrightarrow{A}+\overrightarrow{A}.(\overrightarrow{B}+\overrightarrow{C})+\overrightarrow{B}.\overrightarrow{B}+\overrightarrow{B}.(\overrightarrow{A}+\overrightarrow{C})+\overrightarrow{C}.\overrightarrow{C}+\overrightarrow{C}.(\overrightarrow{A}+\overrightarrow{B})$

$=|\overrightarrow{A}{|}^2+|\overrightarrow{B}{|}^2+|\overrightarrow{C}{|}^2$

$=(3{)}^2+(4{)}^2+(5{)}^2$

$=50$

$|\overrightarrow{A}|+|\overrightarrow{B}|+|\overrightarrow{C}|=\sqrt{50}=5\sqrt{2}$