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

Sicne DC's of ine `OA` are `a/(sqrt(a^(2)+b^(2)+c^(2))),b/(sqrt(a^(2)+b^(2)+c^(2))` and `c/(sqrt(a^(2)+b^(2)+c^(2)))`
Also `vecn=vec(OA)=veca=ahati+bhatj+chatk`
The equation of plane passes through `(a,b,c)` and perpendicular to `OA` is given by
`[vecr.veca].vecn=0`
`impliesvecr.vecn=veca.vecn`
`implies[(xhati+yhatj+zhatk).(ahati+bhatj+chati)]=(ahati+bhatj+chak).(hati+bhatj+chatk)`
`implies ax+by+cz=a^(2)+b^(2)+c^(2)`