Question

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...

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)

Expert Solution

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

milcah answered 3 years ago

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