The points in Cartesian form are,
(2,1,1),(-1,-1,1) and (-1,1,-1)
The equation of plane passing through three points is,
|| x−2 | y−1 | z−1 |
| −1 | −2 | 0 |
| −3 | 0 | −2 |
| =0 Solve the above determinat then,
2x−y−3z=0 The above equation can be expressed in vector form as,
r.(2−−3)=0 If e is unit vector perpendicular to given plane then,
e=| 2−−3 |
| √22+(−1)2+(−3)2 |
=(2−−3) And,
a=2−3+6 The projection of a on e is calculated as,
a.e=+− = The projection vector of a on e is calculated as,
a.e=−((2−−3)) = (−2++3)