If the lines and are perpendicular, find the value of k.


Two lines and

are perpendicular to each other if


a1a2 + b1b2 + c1c2 = 0


Given -



comparing with



we get -


x1 =1, y1 = 2, z1 = 3


& a1 = - 3, b1 = 2k, c1 = 2


Similarly,



comparing with



we get -


x2 = 1, y2 = 2, z2 = 3


& a2 = 3k, b2 = 1, c2 = -5


Since the two lines are perpendicular,


a1a2 + b1b2 + c1c2 = 0


(-3) × 3k + 2k × 1 + 2 × (-5) = 0


-9k + 2k - 10 = 0


-7k = 10


k = -10/7


Hence, the value of k is -10/7.


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