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For the line x11=y22=z33, which one of the following is incorrect ?

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a
it lies in the plane x−2y+z=0
b
it is same as line x1=y2=z3
c
it passes through (2,3,5)
d
it is parallel to the plane x−2y+z=6

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detailed solution

Correct option is C

(1,2,3) satisfies the plane x−2y+z=0  and also  (i^+2j+3k),(i−2j+k)=0Since the lines  x−11=y−22=z−33 and x1=y2=z3both satisfy (0,0,0) and (1,2,3) both are same.  given line is obviously parallel to the plane x−2y+z=6

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