If `O` is the origin and the coordinates of `A` are `(a ,b , c)` . Find the direction cosines of `O A` and the equation of the plane through `A` at right angles to OA.

Explanation

Given,Directional cosine of R is
` a−0,b−0,c−0` or `a,b,c`


∴ Directional cosines of OA are
`a/(a^2+b^2+c^2)`
`b/(a^2+b^2+c^2)​`
`,c/(a^2+b^2+c^2)​​`

Equation of any plane through A, i.e. `(a,b,c)` is

`A(x−a)+B(y−b)+C(z−c)=0.`

But plane is at right angles to
OA which therefore is
normal and whose D.R.'s are `a,b,c.`

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