Question

Find the equation of the plane passing through the point (2, 4, 6) and making equal intercepts on the coordinate axes.

Answer 1

We know that the equation of the plane whose intercepts on the coordinate axes area, bandcis

`x/a + y/b + z/c` = 1

Given that the plane makes equal intercepts on the coordinate axes

So, a = b = c

So, the equation of the plane is 

`x/a + y/a + z/a` = 1

x + y + z = a  ...(1)

This plane passes through the point (2, 4, 6).

Substituting this point in (1), we get

2 + 4 + 6 = a

a = 12

Substituting this in (1), we get

x + y + z = 12