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`

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

Let vec u , vec va n d vec w be such that | vec u|=1,| vec v|=2a n d| vec w|=3. If the projection of vec v along vec u is equal to that of vec w along vec u and vectors vec va n d vec w are perpendicular to each other, then | vec u- vec v+ vec w| equals 2 b. sqrt(7) c. sqrt(14) d. 14

Let vec u , vec va n d vec w be such that | vec u|=1,| vec v|=2a n d| vec w|=3. If the projection of vec v along vec u is equal to that of vec w along vec u and vectors vec va n d vec w are perpendicular to each other, then | vec u- vec v+ vec w| equals 2 b. sqrt(7) c. sqrt(14) d. 14

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 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

Let vec a , vec ba n d vec c be pairwise mutually perpendicular vectors, such that | vec a|=1,| vec b|=2,| vec c|=2. Then find the length of vec a+ vec b+ vec c

If vec a,vec b,vec c are three vectors such that vec a=vec b+vec c and the angle between vec b and vec c is pi/2, then

If vec a ,\ vec b ,\ vec c are three vectors such that vec adot vec b= vec adot vec c then show that vec a=0\ or ,\ vec b=c\ or\ vec a_|_( vec b- vec c)dot

vec a , vec b , vec c are three vectors such that |vec a | = 5 | vec b | =8, |vec c | = 3 if vec a + vec b + vec c = 8 hati+ 6hatj , find the value of vec a , vec b +vec b .vec c + vec c .vec a

Let vec a , vec b ,and vec c be any three vectors, then prove that [ vec axx vec b vec bxx vec c vec cxx vec a ]= [vec a vec b vec c]^2