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Vector Addition

Which of the ...

Question

Which of the following statements are correct:
If in triangle OAC, B is the mid-point of AC and $- - \to O A = \to a$ and $- - \to O B = \to b$ then

A

- - \to O C = \frac{1}{2} (\to a + \to b)

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B

- - \to O C = 2 \to b - 2 \to a

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C

- - \to O C = 2 \to b - \to a

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D

- - \to O C = 3 \to a - 2 \to b

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Solution

The correct option is A $- - \to O C = 2 \to b - \to a$
$B$ is the midpoint of $A C$

$\Rightarrow - - \to O B = \frac{- - \to O A + - - \to O C}{2}$

$∴ - - \to O C = 2 - - \to O B - - - \to O A = 2 \to b - \to a$

Hence, option C.

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