Equation of a line perpendicular to 2 vectors

[Bertrandkis]

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.

 

[HallsofIvy]

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.

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).

But even if you were to find a line perpendicular to V2, there is no reason to think that line would also be perpendicular to V1! You need a direction vector that is perpendicular to both. Do you know how to calculate a vector perpendicular to both V1 and V2?

 

[Bertrandkis]

To be honest, I don't know how to find a vector perpendicular to both V1 and V2.
I can find 2 equations of a lines perpendicular to each of the vectors
(1)=> (x,y,z)=(-1,1,2)+t(-1,1,1)
(2)=> (x,y,z)=(-1,1,2)+t(1,1,1)
now where do I go from here.

 

[HallsofIvy]

Do you know what the cross product of two vectors is?