VectorHard
Question
Let P(3, 2, 6) be a point in space and Q be a point on the line 
. Then the value of μ for which the vector 
is parallel to the plane x - 4y + 3z = 1 is
. Then the value of μ for which the vector is parallel to the plane x - 4y + 3z = 1 isOptions
A.
B.
C.
D.
Solution
Any point on the line can be taken as
Q ≡ {(1-3μ), (μ -1), (5μ + 2)}
= {- 3μ - 2, μ - 3, 5μ - 4}
Now, 1(- 3μ - 2) - 4(μ - 3) + 3 (5μ - 4) = 0
⇒ - 3μ - 2 - 4μ + 12 + 15μ - 12 = 0
8μ = 2 ⇒ μ = 1/4.
Q ≡ {(1-3μ), (μ -1), (5μ + 2)}
= {- 3μ - 2, μ - 3, 5μ - 4}Now, 1(- 3μ - 2) - 4(μ - 3) + 3 (5μ - 4) = 0
⇒ - 3μ - 2 - 4μ + 12 + 15μ - 12 = 0
8μ = 2 ⇒ μ = 1/4.
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