The problem involves finding the equation of a line in R3 that passes through the point (-1,1,2) and is perpendicular to two given vectors, V1 (-1,1,-1) and V2 (1,1,1). The original poster attempts to derive the line's equation in parametric form but expresses uncertainty about the correctness of their approach.
The discussion is ongoing, with participants exploring different approaches to find a suitable direction vector. Some guidance has been offered regarding the need for a vector that is perpendicular to both V1 and V2, and a question about the cross product of the two vectors has been raised.
There is a lack of clarity regarding the method to find a vector that is perpendicular to both V1 and V2, and the original poster expresses confusion about the correctness of their initial solution.
The line you give is not perpendicular to V2. Any point on (-1,1,2)+ t(1,1,1) has position vector (t-1, t+1, t+ 2) and its dot product with (1, 1, 1) is (t-1)+ (t+1)+ (t+2)= 3t+2, not 0. I'm not sure why you think that would give you a line perpendicular to (1,1,1).Bertrandkis said:Homework Statement
Let L be a line in R3 passing through(-1,1,2) and is perpendicular to vectors V1 (-1,1,-1)
and V2 (1,1,1). Find an equation for L in parametric form.
Homework Equations
The Attempt at a Solution
using vector V2
(x,y,z)(1,1,1)=(1,1,1)(-1,1,2)
A possible equation for L=>(x,y,z)=(-1,1,2)+t(1,1,1)
I don't know if I am right.