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Question

The distance of the point P(3,8,2) from the line x12=y34=z23 measured parallel to the plane 3x+2y2z+17=0 is

A
2
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B
3
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C
5
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D
7
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Solution

The correct option is D 7
The equation of plane is 3x+2y2z+17=0
3x+2y2z+c=0 ---- ( 1 )
Substituting Point P(3,8,2) in above equation, we get,
3(3)+2(8)2(2)+c=0
9+164+c=0
c=21
Substituting value of c in equation ( 1 ) we get,
3x+2y2z21=0 ----- ( 2 )

Let, x12=y34=z23=λ
So we get,
x=2λ+1
y=4λ+3
z=3λ+2
Substituting above value in equation ( 2 ) we get,
3(2λ+1)+2(4λ+3)2(3λ+2)21=0
6λ+3+8λ+66λ421=0
8λ=16
λ=2
Now,
x=2λ+1=2(2)+1=5
y=4λ+3=4(2)+3=11
z=3λ+2=3(2)+2=8
Now, we have to find the distance between points (3,8,2) and (5,11,8)=(53)2+(118)2+(82)2
=4+9+36
=49
=7



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