Let ` vec a ,\ vec b ,\ vec c` be three vectors of magnitudes 3, 4 and 5 respectively. If each one is perpendicular to the sum of the other two vectors, prove that `| vec a+ vec b+ vec c|=5sqrt(2)` .

Let vec a , vec b and vec c be three vectors such that | vec a|=3,| vec b|=4,| vec c|=5 and each one of them being perpendicular to the sum of the other two, find | vec a+ vec b+ vec c| .

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

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 ,\ 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\ a n d\ vec b are two vectors of magnitudes 3 and (sqrt(2))/3 respectively such that vec axx vec b is a unit vector. Write the angle between 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| .

Let vec(a), vec(b), vec(c) be vectors of length 3, 4, 5 respectively. Let vec(a) be perpendicular to vec(b)+vec(c), vec(b) to vec(c)+vec(a) and vec(c) to vec(a)+vec(b) . Then |vec(a)+vec(b)+vec(c)| is :

Let vec a , vec b , vec c be three vectors such that | vec a|=1,| vec b|=2a n d| vec c|=3. If the projection of vec b along a is equal to the projection of vec c along vec aa n d vec b , vec c are perpendicular to each other, find |3 vec a-2 vec b+2 vec c|dot

Let vec a , vec b , vec c be the three unit vectors such that vec a+5 vec b+3 vec c= vec0 , then vec a. ( vec bxx vec c) is equal to

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 .