Solution:
(a)
Let the coordinate of the foot of from the origin to the given plane be
The direction ratio are
Now,
On dividing both sides of the eq. (1) by , we obtain
So this is of the form
Where, I, are the direction cosines and is the distance
The direction cosines are
The coordinate of the foot (Id, md, nd) =
(b)
Let the coordinate of the foot of from the origin to the given plane be
The direction ratio are
Now,
The dividing both sides of the eq. (1) by 5 , we obtain
So this is of the form
Where, I, are the direction cosines and is the distance
As a result, the direction cosines are
Coordinate of the foot (Id, md, nd) =