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Question

The ratio in which the plane 2x+3y−2z+7=0 divides the line segment joining the points (−1,1,3), (2,3,5) is

A
3:5
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B
7:5
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C
9:11
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D
1:5 externally
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Solution

The correct option is D 1:5 externally
Let the plane divide the line AB at C in the ratio k:1
The coordinayes of C =(2k1k+1,3k+1k+1,5k+3k+1)
Since this point lies on the plane 2x+3y2z+7=0
Therefore
2(2k1k+1)+3(3k+1k+1)2(5k+3k+1)+7=0
4k2+9k+310k6+7k+7=0
10k+2=0
k=210=15
If the divides the line in the ratio 1:5 externally

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