If the lines (x - 1)/-3 = (y - 2)/2k = (z - 3)/2 and (x - 1)/3k = (y -

1.	If the lines (x - 1)/-3 = (y - 2)/2k = (z - 3)/2 and (x - 1)/3k = (y - 1)/1 = (z - 6)/-5 are perpendicular, find the value of k.
Answer» The direction ratio of two lines are given by(a₁,b₁,c₁) = (-3,2k,2) and (a₂,b₂,c₂) = (3k,1,-5) If the two lines perpendicular than a₁a₂ + b₁b₂+ c₁c₂ = 0 (-3)(3k) + (2k) 1 + (2)(-5) = 0 -9k + 2k - 10 = 0 = -7k - 10 = 0 7k = -10 ∴ k = -10/7

If the lines (x - 1)/-3 = (y - 2)/2k = (z - 3)/2 and (x - 1)/3k = (y - 1)/1 = (z - 6)/-5 are perpendicular, find the value of k.

Answer»

The direction ratio of two lines are given by(a₁,b₁,c₁) = (-3,2k,2) and (a₂,b₂,c₂) = (3k,1,-5)

If the two lines perpendicular than a₁a₂ + b₁b₂+ c₁c₂ = 0

(-3)(3k) + (2k) 1 + (2)(-5) = 0

-9k + 2k - 10 = 0

= -7k - 10 = 0

7k = -10

∴ k = -10/7