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Question

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

A
3:2 internally
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B
3:2 externally
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C
2:1 internally
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D
2:1 externally
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Solution

The correct option is B 3:2 externally
Let R divides PQ in ratio m:n.
By Section Formula
coordinates of R are:
R=(5m+3nm+n,4m+2nm+n,6m4nm+n)

we have coordinates of R=(9,8,-10)
Therefore,
9=5m+3nm+n
9m+9n=5m+3n
6n=4m
mn=32
Therefore R divides PQ in 3:2 ratio and negative sign indicates,it cuts Externally.
Therefore option (B) is Correct.

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