If the lines x - 3 2 = y - 5 2 = z - 4 λ and x - 2 λ = y - 6 4 = z - 5 2 intersect at a point α , β , γ , then the greatest value of λ is equal to

Question

If the lines x - 3 2 = y - 5 2 = z - 4 λ and x - 2 λ = y - 6 4 = z - 5 2 intersect at a point α , β , γ , then the greatest value of λ is equal to, 0, 2, - 2, 4

MARKS App · Accepted Answer

Two given lines intersect ⇒ they must be coplanar So, 3 - 2 5 - 6 4 - 5 2 2 λ λ 4 2 = 0 ⇒ 1 4 - 4 λ + 1 4 - λ 2 - 1 8 - 2 λ = 0 ⇒ 4 - 4 λ + 4 - λ 2 - 8 + 2 λ = 0 ⇒ λ 2 + 2 λ = 0 ⇒ λ = 0 , - 2

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