If from a point `P(a ,b ,c)` perpendiculars `P Aa n dP B` are drawn to `Y Za n dZ X-p l a n e s` find the vectors equation of the plane `O A Bdot`

Explanation

The coordinates of the point A and B are (0,b,c) and (a,0,c) respectively.
`:. bar(OA)= b hatj+hatk`
and `bar(OB)= ahati+chatk`
The plane, OAB passes through point `O(barO)` and is perpendicular to `barn=bar(OA)xxbar(OB)`
`:. bar n= bar(OA)xxbar(OB)=|{:(hati,hatj,hatk),(0,b,c),(a,0,c):}|`
`= bc hati+achatj-abhatk`
`:.` The equation of the plane OAB is
`(barr-bar0)*barn=0`
`:. vecr*vecn=0`
`:. vecr(bc bari+ac barj-ab bark)=0`