Question

Which of the sets given below may represent the magnitude of three vectors adding to zero?

• A. $2,4,8$
• B. $4,8,16$
• C. $1,2,1$
• D. $0.5,1,2$

Answer 1

The correct option is C $1,2,1$

Given that the three vectors adding to zero.
$\Rightarrow \overrightarrow{A}+\overrightarrow{B}+\overrightarrow{C}=0$
$\Rightarrow \overrightarrow{C}=-(\overrightarrow{A}+\overrightarrow{B})$
$\Rightarrow |\overrightarrow{C}|=|-(\overrightarrow{A}+\overrightarrow{B})|$
$\Rightarrow A-B\le C\le A+B$
Thus, the magnitude of third vector should be less than or equal to the sum of other two vectors or greater than or equal to the difference of other two vectors.
This condition is only satisfied in option $\left(c\right)$. Hence, option $\left(c\right)$ is the correct answer.