Thread: Simple 3D Vector geometry question about planes and lines!

How would you find the vector equation of the line h, if told it lies in the plane:

E: x plus y = 4,

and it passes through Q(2,2,1) which is on the plane,

and the line is also perpendicular to the line -->


g = (1 plus µ)i plus (3-µ)j plus (3)k



find line h.



please help!!! thanks!!!

Originally Posted by Yehia

How would you find the vector equation of the line h, if told it lies in the plane:

E: x plus y = 4, and it passes through Q(2,2,1) which is on the plane,

and the line is also perpendicular to the line -->


g = (1 plus µ)i plus (3-µ)j plus (3)k

Find line h.

1. Not sure in which part of Germany you live but where I live we would use this notation:





2. You are looking for a point P with the following properties:



That means the distance has a minimum.

There is a simple formula which yields the perpendicular distance of a point to a straight line which is probably known to you. I'll show you a different approach (it is always useful to have an alternative at hand ) :

3. Calculate the vector from Q to any point of g:





Determine the minimum of by differentiating wrt and set the numerator of the quotient equal to zero.
You'll get which produces the point P(2,2,3).

4. Thus the line you are looking for is the line .