The number of real values of k for which the lines x-k 4 = y-1 2 = z+1 1 and x-(k+1) 1 = y -1 = z-1 2 are intersecting, is

JEE Advanced Mathematics question

The number of real values of for which the lines and are intersecting, is

Answer: (D)

A general point on the first line is , and on the second . They meet if, for some ,

4r+k=r'+k+1, 2r+1=-r', r-1=2r'+1 4r-r'=1, 2r+r'=-1, r-2r'=2 .

Adding the first two gives , so

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Question ID VK-109844