find a point on the plane x+y+z=1 that

Answered question

2022-04-17

find a point on the plane x+y+z=1 that is closest to the point (2,0,-3)

Answer & Explanation

nick1337

nick1337

Expert2022-07-19Added 777 answers

The normal vector to the plane is 1,1,1. The point you seek would have to be some multiple of this vector added to (2,0,-3).

P=(2,0,-3)+c1,1,1=(2+c, c, 3-c)
But this point has to satisfy the plane's equation:

(2+c)+(c)+(3-c)=12c+5=1c=42 с=-2

So

P=(2,0,-3)21,1,1=(-2,-2,-2)

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?