If a vector ` vec a` is perpendicular to two non-collinear vector ` vec b` and ` vec c` , then ` vec a` is perpendicular to every vector in the plane of ` vec b` and ` vec c` .

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

Let vec a , vec b , and vec c are vectors such that | vec a|=3,| vec b|=4 and | vec c|=5, and ( vec a+ vec b) is perpendicular to vec c ,( vec b+ vec c) is perpendicular to vec a and ( vec c+ vec a) is perpendicular to vec bdot Then find the value of | vec a+ vec b+ vec c| .

If vec c is perpendicular to both vec a and vec b , then prove that it is perpendicular to both vec a+ vec b and vec a - vec b .

If vec a\ a n d\ vec b are mutually perpendicular unit vectors, write the value of | vec a+ vec b|dot

If vec c is a unit vector perpendicular to the vectors vec a\ a n d\ vec b write another unit vector perpendicular vec a\ a n d\ vec bdot

If vec a , vec b are two vectors such that | vec a+ vec b|=| vec b|, then prove that vec a+2 vec b is perpendicular to vec a .

If vec a ,\ vec b are two vectors such that | vec a+ vec b|\ =| vec b|, then prove that vec a+2 vec b is perpendicular to vec adot

If vec a , vec b , vec c are mutually perpendicular unit vectors, find |2 vec a+ vec b+ vec c|dot

If vec a ,\ vec b ,\ are two vectors such that | vec a+ vec b|=| vec a|, then prove that 2 vec a+ vec b is perpendicular to vec bdot

If vec a ,\ vec b ,\ vec c are three mutually perpendicular unit vectors, then prove that | vec a+ vec b+ vec c|=sqrt(3)