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Linear Algebra planes in 4d 
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#1
May911, 09:44 PM

P: 1

1. The problem statement, all variables and given/known data
I am given two lines in vector form in 4space. I need to write an equation for the plane that is parallel to one line, and contains the other line. 2. Relevant equations well i know that in 3d I would find a normal vector for the plane that would be perpendicular to both lines, and that would let me define the plane. However i am stumped because in 4space there are an infinite amount of vectors that are perpendicular to both lines. 3. The attempt at a solution I took the dot product of the vectors and got an infinite number of possible normals. I know one point on the plane from the line that is contained in the plane, all i need is another vector in the plane to define it but I cannot figure it out. I didn't want to give the numbers here because i can find it out on my own once I am given some direction. 


#2
May1011, 12:22 AM

Sci Advisor
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P: 4,300

In this case, the space of vectors which is perpendicular to both lines is just twodimensional, instead of one. For example, for the (x, y) plane the perpendicular vectors would be (0, 0, z, u) for z.u not equal to 0. 


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