Question

The direction ratios of the normal to the plane passing through origin and the line of intersection of the planes x + 2y + 3z = 4 and 4x + 3y + 2z = 1 are ______.

पर्याय

• 2, 3, 1

• 1, 2, 3

• 3, 1, 2

• 3, 2, 1

Answer 1

The direction ratios of the normal to the plane passing through origin and the line of intersection of the planes x + 2y + 3z = 4 and 4x + 3y + 2z = 1 are 3, 2, 1.

Explanation:

We have, line of intersection of the planes

x + 2y + 3z = 4 and 4x + 3y + 2z = 1

∴ Equation of plane passing through the given planes is

(x + 2y + 3z - 4) + λ(4x + 3y + 2z - 1) = 0

⇒ (1 + 4λ)x + (2 + 3λ)y + (3 + 2λ) + (- 4 - λ) = 0

Since, plane passing through origin

∴ - 4 - λ = 0 ⇒ λ = - 4

Now, equation of plane is

(1 - 16)x + (2 - 12)y + (3 - 8)z+ 0 = 0

⇒ - 15x - 10y - 5z = 0

⇒ 3x + 2y + z = 0

∴ Direction ratios of the normal to the plane are 3, 2, 1.