Question

# If →a and →b are the position vectors of points A and B respectively, find the position vector of point C on AB produced such that →AC=3→AB

A
2a3b
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B
3a2b
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C
3b2a
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D
2b3a
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Solution

## The correct option is C 3→b−2→a It is given in the question that →AC=3→AB →BC=→AC−→AB →BC=3→AB−→AB (→AC=3→AB) →BC=2→AB Now ACBC=|→AC||→BC|=|3→AB||2→AB|=32|→AB||→AB|=32 So C divides AB in the ratio 3:2 externally. And we know that position vector of point P dividing →AB externally in the ratio m:n is given by m→B−n→Am−n Therefore the position vector of C is given by, →r=3→b−2→a3−2=3→b−2→a, which is the correct answer.

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