If ` vec c` is perpendicular to both ` vec a\ a n d\ vec b ,` then prove that it is perpendicular to both ` vec a+ vec b\ a n d\ vec a- vec bdot`

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 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

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 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 , vec c be three non-zero vectors such that vec c is a unit vector perpendicular to both vec aa n d vec b . If the between vec aa n d vec b is pi//6 , prove that [ vec a vec b vec c]^2=1/4| vec a|^2| vec b|^2dot

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

Find | vec a|a n d\ | vec b| , if : ( vec a+ vec b)dot'( vec a- vec b)=8\ a n d\ | vec a|=8| vec b|

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 is perpendicular to vec b and vec r is non-zero vector such that p vec r+( vec rdot vec a) vec b= vec c , then vec r= vec c/p-(( vec adot vec c) vec b)/(p^2) (b) vec a/p-(( vec cdot vec b) vec a)/(p^2) vec a/p-(( vec adot vec b) vec c)/(p^2) (d) vec c/(p^2)-(( vec adot vec c) vec b)/p