Question

Find the equation of the plane containing points (3,0,0), (0,8,0) and (0,0,6)

Answer 1

A plane has equation
`ax+by+cz=d`. With the given information, you should be able to find the values of
`a,b,c,d`.

Since the plane contains the points
`(3,0,0)`, you have


`a*3+b*0+c*0=3a=d`

The other points tell you that you have


`8b=d`

`6c=d`

So,
`3a=8b=6c`, or, fixing
`a`, you get
`b=\frac38a`,
`c=\frac12a`, and
`d=3a`, giving the equation


`ax+\frac38ay+\frac12az=3a\implies x+\frac38y+\frac12z=3\implies 8x+3y+4z=24`