Mark the correct alternative in each of the following:
The unit vector perpendicular to the plane passing through points and
is
The equations of the plane is given by
A(x-x1)+B(y-y1)+C(z-z1)=0
Where A,B and C are the drs of the normal to the plane.
Putting the first point,
=A(x-1)+B(y+1)+C(z-2)=0 …(1)
Putting the second point in Eqn (1)
=A(2-1)+B(0+1)+C(-1-2)=0
A+B-3C=0 …(a)
Putting the third point in Eqn (1)
=A(0-1)+B(2+1)+C(1-2)=0
= -A+3B-C=0 …(b)
Solving (a) and (b) using cross multiplication method
A+B-3C=0
-A+3B-C=0
Put these in Eqn(1)
=8α(x-1)+4α(y+1)+4α(z-2)=0
=2(x-1)+(y+1)+(z-2)=0
=2x+2+y+1+z-2=0
2x+y+z+1=0
Now the vector perpendicular to this plane is
Now the unit vector of is given by
(
(C)