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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