Q.

Let the position vectors of two points A and B be a+b+c and a-2b+3c respectively. If the points P and Q divide AB in the ratio 1:3 internally and externally respectively, they 3AB=

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a

PQ

b

3PQ

c

4PQ

d

12PQ

answer is A.

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Detailed Solution

OP=a-2b+3c+3a+3b+3c4=4a+b+bc4 OQ =a-2b+3c-3a-3b-3c-2=-2a-5b-2 3AB=3-3b+2c                    =2a+5b2 PQ=9b-6c                            =4a+10b4

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