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Question

If the points P(3,2,4),Q(9,8,10) and R(5,4,6) are collinear, then R divides PQ in the ratio

A
1:2
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B
1:2
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C
2:1
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D
2:1
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Solution

The correct option is B 1:2
Given P(3,2,4)
Q(9,8,10)R(5,4,6)
are collinear so
R divides PQ externally & internally.
P(x,y,z)=(mx2+nx1m+n,my2+ny1m+n)
so (x,y,z)=(5,4,6)
(x1,y1,z1)=(3,2,4)
(x2,y2,z2)=(9,8,10)
Ratio k:1=m:n
So:-
Q(5,4,6)=(k(9)+3k+1,k(8)+2k+1,k(10)4k+1)
(5,4,6)=(9k+3k+1,8k+2k+1,10k4k+1)
So :- 9k+3k+1=5
9k+3=5k+5
4k=2
k=2/4=12
k:1=1:2
R divides PQ in Ratio 1:2.

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