Let A be a point on the line and B (3, 2, 6) be a point in the space. Then the value of μ for which the vector is parallel to the plane x

Engineering

Mathematics

Plane and Its Different Forms

Question

Let A be a point on the line $\vec{r} = (1 - 3 μ) \hat{i} + (μ - 1) \hat{j} + (2 + 5 μ) \hat{k}$ and B (3, 2, 6) be a point in the space. Then the value of μ for which the vector $\vec{AB}$ is parallel to the plane x – 4y + 3z = 1 is

$\frac{1}{2}$

$\frac{1}{4}$

$\frac{- 1}{4}$

$\frac{1}{8}$

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Let A is (1– 3μ, μ –1, 2 + 5μ)

$\overset{⇀}{AB}$ = (3μ + 2)i + (3 – μ) j + (4 – 5μ)

$\hat{k}$ which is parallel to plane x – 4y + 3z = 1

⇒ 1(3μ + 2) – 4(3 – μ) + 3(4 – 5μ) = 0

$= - 8 μ + 2 = 0 \Rightarrow μ = \frac{1}{4}$