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Question

Line passing through the point 2¯¯¯a+3¯¯b¯¯c,3¯¯¯a+4¯¯b2¯¯c intersects the line passing through the point ¯¯¯a2¯¯b+3¯¯c,¯¯¯a6¯¯b+6¯¯c at P. Position vector of P=

A
2¯¯¯a+¯¯b
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B
¯¯¯a+2¯¯b
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C
3¯¯¯a+4¯¯b
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D
¯¯¯a2¯¯b
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Solution

The correct option is B ¯¯¯a+2¯¯b
Let line passing through (2,3,1) and (3,4,2) be
x21=y31=z+11=α (Let)
So, x=α+2,y=α+3,z=α1
and line passing through (1,2,3) and (1,6,6) be
x10=y+24=z33=β (Let)
On comparing we get
x10=βx=1x=2+α=1α=1y=α+3=2z=α1=0
So, P(+1,2,0)
Then position vector of P=¯a+2¯b

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