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Question

The lines x1=y2=z3 and x-1-2=y-2-4=z-3-6 are
(a) parallel
(b) intersecting
(c) skew
(d) coincident

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Solution

(d) coincident

The equations of the given lines are

x1=y2=z3 ...(1)


x-1-2=y-2-4=z-3-6x-11=y-22=z-33 ...2

Thus, the two lines are parallel to the vector b=i^+2j^+3k^ and pass through the points (0, 0, 0) and (1, 2, 3).

Now,

a2-a1×b=i^+2j^+3k^×i^+2j^+3k^ =0 a×a=0

Since, the distance between the two parallel lines is 0, the given two lines are coincident lines.


Disclaimer: The answer given in the book is incorrect. This solution is created according to the question given in the book.

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