Find the coordinates of the point (x,y,z) on the plane z = x + 3y + 3 which is ...

Question: Find the coordinates of the point (x,y,z) on the plane z = x + 3y + 3 which is closest to the origin.

Answer:

x = -0.272727272727273

y = -0.818181818181818

z = 0.272727272727273

Please show me how to do this problem!

Any help would be appreciated!

Thanks in advance!

Re: Find the coordinates of the point (x,y,z) on the plane z = x + 3y + 3 which is ..

Re: Find the coordinates of the point (x,y,z) on the plane z = x + 3y + 3 which is ..

Quote:

Originally Posted by

**s3a** Question: Find the coordinates of the point (x,y,z) on the plane z = x + 3y + 3 which is closest to the origin.

Answer:

x = -0.272727272727273

y = -0.818181818181818

z = 0.272727272727273

Please show me how to do this problem!

Any help would be appreciated!

Thanks in advance!

Search the minimum of the function...

... respect to x and y...

Kind regards

Re: Find the coordinates of the point (x,y,z) on the plane z = x + 3y + 3 which is ..

Sorry for the stupid question but how do I know that f(x,y) = x^2 + y^2 + z^2 is what I want to minimize?

Re: Find the coordinates of the point (x,y,z) on the plane z = x + 3y + 3 which is ..

Quote:

Originally Posted by

**s3a** Sorry for the stupid question but how do I know that f(x,y) = x^2 + y^2 + z^2 is what I want to minimize?

Because is the square of the distance of the point from the origin.

Re: Find the coordinates of the point (x,y,z) on the plane z = x + 3y + 3 which is ..

Quote:

Originally Posted by

**s3a** Question: Find the coordinates of the point (x,y,z) on the plane z = x + 3y + 3 which is closest to the origin.

Answer:

x = -0.272727272727273

y = -0.818181818181818

z = 0.272727272727273

**One does not need any calculus to solve this.**

The plane is .

Find out where the __line__ __intersects that plane.__