If a vector ` vec a` is perpendicular to two non collinear vectors ` vec b\ a n d\ vec c ,\ t h e n\ \ vec a\ ` is perpendicular to every vector in the plane of`\ vec b\ a n d\ vec c`

Explanation

vector ` vec a`
is perpendicular to two non collinear vectors ` vec b\ a n d\ vec c `
` vec d = x vec b +y vec c`
`=> vec a* vec d = x vec a* vec b + y vec a* vec c`
`=>vec a* vec d=0`
`=>"every vector in plane of vec b and vec c is perpendicular to vec a"`