Find the vector equation of the plane passing through the points `A(a ,0,0),B(0,b ,0)a n dC(0,0,c)dot` Reduce it to normal form. If plane `A B C` is at a distance `p` from the origin, prove that `1/(p^2)=1/(a^2)+1/(b^2)+1/(c^2)dot`

Explanation

Given,


The two vectors lying in plane are

`1) bj​−ai`

`2) ck−bj​`

Thus Normal vector to plane is
`(bj−ai)×(ck−bj​)=(bci+acj​+abk)`


One point on plane is ai^\
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