The equation of the plane, parallel to t

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Three-dimensional Geometry

Question:

The equation of the plane, parallel to the plane 3x + 4y - 12z =3 and passes through (1, 1, -1), is

Options:

3x + 4y - 12z = 0

3x + 4y + 12z = 3

3x + 4y - 12z = 19

3x + 4y - 12z = 22

Correct Answer:

3x + 4y - 12z = 19

Explanation:

Equation of plane parallel to 3x + 4y −12z = 0 is given by,

$3x + 4y −12z+λ=0$

It passes through (1, 2, 3)

$⇒3(1)+4(1)−12(1)+λ=0⇒3+4+λ=0$

$λ=0-19⇒λ=-19$

∴ required plane is

$3x + 4y −12z -19= 0$

$⇒3x + 4y −12z =19$