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Vector Addition

Which of the ...

Question

Which of the following statements are correct:
If $M$ is the mid-point of $A B$ and $O$ is any point then

- - \to O M = - - \to O A + - - \to M A

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- - \to O M = - - \to O A - - - \to M A

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- - \to O M = \frac{1}{2} (- - \to O A - - - \to O B)

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- - \to O M = \frac{1}{2} (- - \to O B + - - \to O A)

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Solution

The correct options are
B $- - \to O M = - - \to O A - - - \to M A$
C $- - \to O M = \frac{1}{2} (- - \to O B + - - \to O A)$
Given, M is the mid-point of AB.
$- - \to O M = - - \to O A + - - \to A M = - - \to O A - - - \to M A$
$- - \to A M = - - \to M B$
$\Rightarrow - - \to O M - - - \to O A = - - \to O B - - - \to O M$
$\Rightarrow - - \to O M = \frac{- - \to O A + - - \to O B}{2}$
Hence, options B and D.

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