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Show that the lines `("x"-1)/(3) = ("y"-1)/(-1) = ("z"+1)/(0) = λ and ("x"-4)/(2) = ("y")/(0) = ("z"+1)/(3)` intersect. Find their point of intersection.

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#### Solution

`(x - 1)/3 = (y - 1)/(-1) = (z + 1)/0 = λ ("let") ....(i)`

⇒ x = 3λ + 1, y = - λ + 1, z = - 1

`(x - 4)/2 = y/0 = (z + 1)/3 = mu ....(ii)`

⇒ x = 2μ + 4, y = 0, z = 3μ - 1

If the lines intersect, then they have a common point for some value of λ and μ.

So, 3λ + 1 = 2μ + 4 ....(iii)

- λ + 1 = 0 ⇒ λ = 1

3μ + 1 = - 1 ⇒ μ = 0

Since λ = 1 & μ = 0 satisfy equation (iii) so the given lines intersect and the point of intersection is (4, 0, – 1).

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