Question

If the plane 2x + 3y + 5z = 1 intersects the co-ordinate axes at the points A, B, C, then the centroid of Δ ABC is ______.

Options

• (2, 3, 5)

• `(1/6, 1/9, 1/15)`

• `(3/2, 1, 3/5)`

• `(1/2, 1/3, 1/5)`

Answer 1

If the plane 2x + 3y + 5z = 1 intersects the co-ordinate axes at the points A, B, C, then the centroid of Δ ABC is `underline(1/6, 1/9, 1/15).`

Explanation:

Given plane,

2x + 3y + 5z = 1 intersects the co-ordinate axes at the points A, B, C

∴ Equation of plane in intercept form is,

`x/(1//2) + y/(1//3) + z/(1//5) = 1`

∴ `"A"(1/2,0,0), "B"(0,1/3,0), "C"(0,0,1/5)`

∴ Centroid of Δ ABC is `(1/6, 1/9, 1/15)`