Thread: Linear algebra, finding a subset which is perpendicular to another

M is a subset of R^n. We denote the set of vectors which are perpendicular to M as M* (ie each element of M* is perpendicular to each element of M).

(Question) In R^3, find M* where M={2i-j+2k,i-2j-2k}.

Hello,

Originally Posted by flawless

M is a subset of R^n. We denote the set of vectors which are perpendicular to M as M* (ie each element of M* is perpendicular to each element of M).

(Question) In R^3, find M* where M={2i-j+2k,i-2j-2k}.

Do you know things about the cross product ?

Here, you have , where :

and


will be perpendicular to both u and v.



(the first coordinate was obtained by ignoring the line composed of the first coordinates of u and v, then we take the determinant of the remainder... etc for second and third)



So, unless I've made mistakes :