If P is (3, 2, 6) is a point in space and Q be a point on the line r = (i - j + 2k) + μ(-3i + j + 5k). Then, the value of μ for which the vector overrightarrowPQ is parallel to the plane x - 4y + 3z = 1, is

If P is (3, 2, 6) is a point in space and Q be a point on… — JEE Main 2009 Mathematics PYQ

AIEEE 2009

P

(3, 2, 6)

is a point in space and

Q

be a point on the line

\vec{r} = (\hat{i} - \hat{j} + 2\hat{k}) + \mu(-3\hat{i} + \hat{j} + 5\hat{k})

. Then, the value of

\mu

for which the vector

\overrightarrow{PQ}

is parallel to the plane

x - 4y + 3z = 1

, is

A.
$\dfrac{1}{4}$
B.
$-\dfrac{1}{4}$
C.
$\dfrac{1}{8}$
D.
$-\dfrac{1}{8}$

Show answer and solution

Correct option: A

Solution

Q = (1 - 3μ, -1 + μ, 2 + 5μ)

PQ = Q - P = (1 - 3μ - 3, -1 + μ - 2, 2 + 5μ - 6) = (-2 - 3μ, -3 + μ, -4 + 5μ)

For PQ to be parallel to the plane x - 4y + 3z = 1, PQ must be perpendicular to the plane's normal (1, -4, 3).

PQ · n = 0:
1(-2 - 3μ) + (-4)(-3 + μ) + 3(-4 + 5μ) = 0
-2 - 3μ + 12 - 4μ - 12 + 15μ = 0
(-2 + 12 - 12) + (-3 - 4 + 15)μ = 0
-2 + 8μ = 0
μ = 1/4

[AIEEE 2009]

Practise Three Dimensional Geometry the way it is asked

A timed set of real JEE Main Three Dimensional Geometry questions, graded as the exam grades. No sign-up.

Start a Three Dimensional Geometry test

More: all JEE Main Three Dimensional Geometry questions · JEE Main 2009 · Mathematics chapter list

JEE Main 2009 Mathematics question on Three Dimensional Geometry