In: Math
a. consider the plane with equation -x+y-z=2, and let p be the point (3,2,1)in R^3. find the distance from P to the plane.
b. let P be the plane with normal vector n (1,-3,2) which passes through the point(1,1,1). find the point in the plane which is closest to (2,2,3)
a. The distnace of the point from the plane is
here we have plane ,
point ,
we get distance as
b. we have normal vector on plane as
and it passes through
we get equation of the plane as
we find a line containing the point and direction ratio same as normal vector ,
plugging this into plane equation we get
plugging this value of t in line equation we get
so the closest point on plane is