Question

The equation of line vector L1, is in R^3, and L1=<-3,5,7>k+<1,-2,0>

Determine algebraically the scalar equation of a plane in R^3 that does NOT intersect this line

Answer 1

you don't have unique solution for this plane.

Answer 2

take any line not intersecting this line. make tangent on that plane is parallel to that line.

Answer 3

So I have to find a line that is parallel to L1, and then find a plane that contains that parallel line, I'm just not sure how to do the second part algebraically

Answer 4

I gave an answer for this yesterday. As experiment x says, there are infinite solutions.

Answer 5

choose any point particularly that does not line on your line.

Answer 6

here's how I would do it:
given the line L1=<a,b,c>k+Po
the direction vector is v=<a,b,c>
create another vector u=<n,m,c> (that is, keep one component the same)
then vk+Po and uk+Po will lie in the same plane
cross v and u to find the normal vector of the plane in which the two lines lie n

now write out the equation for the plane using a point that is a constant scalar multiple of the original Po (such as A*Po)

n(dot)P=n(dot)A*Po where P=<x,y,z>

by construction this plane will not intersect the original line, as it is parallel to the original line and does not contain the point initially given Po

Answer 7

I'm trying to draw the other one so it looks like it has the same z-component. Not easy to do in three space.

Answer 8

some plane contains these linescross the two vectors that point along the two line to find the normal vector to the plane

Answer 9

now create a plane, basing n at any other point