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Vector Triple Product

If a and ...

Question

If $¯ ¯ ¯ a$ and $¯ ¯ b$ are position vectors of $A$ and $B$ respectively, then the position vector of a point $C$ in $A B$ produced such that $¯ ¯¯¯¯¯¯ ¯ A C = 3 ¯ ¯¯¯¯¯¯ ¯ A B$ is

3 ¯ ¯ ¯ a - ¯ ¯ b

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3 ¯ ¯ b - ¯ ¯ ¯ a

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3 ¯ ¯ ¯ a - 2 ¯ ¯ b

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3 ¯ ¯ b - 2 ¯ ¯ ¯ a

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Solution

The correct option is B $3 ¯ ¯ b - 2 ¯ ¯ ¯ a$
Let the Position Vector of $C$ be $\to c$
We have $\to A C = 3 \to A B$
$\to c - \to a = 3 (\to b - \to a)$
$\to c = 3 \to b - 2 \to a$

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