A plane P meets the coordinate axes at A, B and C respectively.

Question

A plane $P$ meets the coordinate axes at $A$, $B$ and $C$ respectively. The centroid of $	riangle ABC$ is given to be $(1,1,2)$. Then the equation of the line through this centroid and perpendicular to the plane $P$ is:

Accepted Answer

Let, Equation of plane is

$${x \over a} + {y \over b} + {z \over c}$$ = 1

A = ($a$, 0, 0) B
= (0, b, 0), C
= (0, 0, c)

$$ \therefore $$ Centroid = $$\left( {{a \over 3},{b \over 3},{c \over 3}} \right)$$ = (1, 1, 2)

$$ \Rightarrow $$ $a$ = 3, b = 3, c = 6

$$ \therefore $$ Plane : $${x \over 3} + {y \over 3} + {z \over 6}$$ = 1

$$ \Rightarrow $$ 2x + 2y + z = 6

The equation of the
line through this centroid (1, 1, 2) and
perpendicular to
the plane 2x + 2y + z = 6 is :

$${{x - 1} \over 2} = {{y - 1} \over 2} = {{z - 2} \over 1}$$

Solutions · 1