Vector 3DHard
Question
If the shortest distance between the lines 
(α ≠ − 1) and x + y + z + 1 = 0 = 2x − y +z + 3 is
, then a value of α is :
(α ≠ − 1) and x + y + z + 1 = 0 = 2x − y +z + 3 is, then a value of α is :Options
A.
B.
C.−
D.
Solution
Any plane x + y + z (2x - y + z + 3) = 0
⇒ (2 λ + 1)x + (1 - λ)y + (1 + λ)z + 3 λ + 1 = 0
parallel to given line if
α (2 λ + 1) - 1(1 - λ) + 1.(1 + λ) = 0
⇒ α =
......(1)
by (1)
Also
⇒ λ = 0,
α = 0, or α = 
⇒ (2 λ + 1)x + (1 - λ)y + (1 + λ)z + 3 λ + 1 = 0
parallel to given line if
α (2 λ + 1) - 1(1 - λ) + 1.(1 + λ) = 0
⇒ α =
......(1)by (1)
Also
⇒ λ = 0,
α = 0, or α = Create a free account to view solution
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