Question

A Plane cuts the coordinate axes X, Y, Z at A, B, C respectively such that the centroid of the Δ ABC is (6, 6, 3). Then the equation of that plane is ______.

विकल्प

• x + y + z - 6 = 0

• x + 2y + z - 18 = 0

• 2x + y + z - 18 = 0

• x + y + 2z - 18 = 0

Answer 1

A Plane cuts the coordinate axes X, Y, Z at A, B, C respectively such that the centroid of the Δ ABC is (6, 6, 3). Then the equation of that plane is x + y + 2z - 18 = 0.

Explanation:

Let A ≡ (a, 0, 0), B ≡ (0, b, 0) and C ≡ (0, 0, c)

The equation of the plane in intercept form is `x/"a" + "y"/"b" + "z"/"c" = 1`

Since, centriod is (6, 6, 3)

`therefore 6 = (x_1 + x_2 + x_3)/3`

`=> 6 = ("a" + 0 + 0)/3 => "a" = 18`

Similarly `(0 + "b" + 0)/3 = 6 => "b" = 18`

`(0 + 0 + "c")/3 = 3 => "c" = 9`

∴ The equation of plane is `x/"a" + "y"/"b" + "z"/"c" = 1`

⇒ x + y + 2z - 18 = 0