Question

A plane intersects the x,y,z axis at A.B. C respectively. If G(1,1,2) is the centroid of ΔABC, then the equation of the line perpendicular to plane and passing through G is?

Answer 1

A plane intersects the x, y, z axis at A, B, C respectively. G(1, 1, 2) is the centroid of ∆ABC.

To find : The equation of the line perpendicular to plane and passing through G is...

solution : Let a plane intersects x - axis at A(α, 0, 0), intersects y - axis at B(0, β, 0) and intersects z - axis at C(0, 0, γ)

centroid of ∆ABC = [(α + 0 + 0)/3, (0 + β + 0)/3, (0 + 0 + γ)/3 ] = [α/3, β/3, γ/3] = (1, 1, 2)

⇒α = 3, β = 3 and γ = 6

equation of plane is x/α + y/β + z/γ = 1

⇒x/3 + y/3 + z/6 = 1

⇒2x/6 + 2y/6 + z/6 = 1

⇒2x + 2y + z = 6 ........(1)

direction ratios 2, 2, 1

now equation of required line passing through (1,1,2),

(x - 1)/2 = (y - 1)/2 = (z - 2)/1

Therefore the correct option is (3)

Answer 2

$\huge\boxed{\fcolorbox{white}{pink}{Answer}}$

A(a,0,0),B(0,b,0),C(0,0,c) are the points on coordinate axis and centriod (α,β,γ).

According to centroid formula,

α=

3

a

a=3α

b=3β

c=3γ

______________

ɧσ℘ε ıt'ร ɧεɭ℘ʄนɭ ❤️