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Applications of Cross Product

If a and ...

Question

If $\to a$ and $\to b$ are postion vectors of A and B respectively, then the position vector of a point C in AB produced such that $- - \to A C = 3 - - \to A B$ is:

3 \to a - \to b

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3 \to b - \to a

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3 \to a - 2 \to b

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3 \to b - 2 \to a

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Solution

The correct option is A $3 \to b - 2 \to a$
$\to A C = 3 \to A B$

$\to O C - \to O A = 3 (\to O B - \to O A)$

$\begin{matrix} - - \to O C - - - \to O A = 3 - - \to O B - 3 - - \to O A - - \to O C = 3 - - \to O B - 2 - - \to O A - - \to O C = 3 \to b - \to a \end{matrix}$

Therefore, position vector of point $C$ is $3 \to b - 2 \to a$

Hence, option $D$ is the correct answer.

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Similar questions

If a and b are the position vectors of two points A and B and C is a point on AB produced such that AC = 3AB, then position vector of C will be

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