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Q.

For the line  x22=y33=z44,  which one of the following  is INCORRECT ?

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a

It is parallel to the line  r=(1,1,1)+λ(4,6,8)

b

It lies in the plane  x2y+z=0

c

It is parallel to the plane  x2y+z=10

d

It is same as line  x1=y2=z3

answer is D.

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Detailed Solution

 r=(1,1,1)+λ(4,6,8)  as  4i+6j=8k=2(2i+3j+4k)
as  2(2i+3j+4k).(i2j+k)=26+4=0
as point (2,3,4) satisfies the plane  x2y+z=0
It is of course parallel to the plane  x2y+z=10
Line  x2=y3=z4  satisfied by both points (0,0,0) and (2,3,4).

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