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Question

If a, b are the position vectors of A, B respectively, find the position vector of a point C in AB produced such that AC = 3 AB and that a point D in BA produced such that BD = 2BA.

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Solution


Let the position vectors of C and D are c and d respectively. We have,
AC=3 AB. AC = 3 (AC-BC).2AC =3BC.
ACBC = 32.
So C divides AB in the ratio of 3:2 externally.
c = 2a- 3b 2-3 = 3b- 2a.

Position vector of point C is 3b-2a
Moreover,
BD = 2 BA.BD = 2(BD-AD). BD = 2AD.
BDAD = 21.
d = b- 2a1-2= 2a - b.
Position vector of point D is 2a-b

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