If `|vec a| = 2, |vec b| = 5` and `|vec a xx vec b| = 8` , find the value of `vec a. vecb`

If | vec a|=| vec b|=| vec a+ vec b|=1, then find the value of | vec a- vec b|dot

If vec a and vec b are two vectors such that | vec axx vec b|=2, then find the value of [ vec a vec b vec axx vec b].

If vec a, vec b, vec c are unit vectors such that vec a+ vec b+ vec c =0 , find the value of vec a.vec b+ vec b .vec c + vec c. vec a .

If |vec(a)| = 13, |vec(b)| = 5 and vec(a) cdot vec(b) = 60 then |vec(a) xx vec(b)| is

Given | vec a|=| vec b|=1a n d| vec a+ vec b|=sqrt(3). If vec c is a vector such that vec c- vec a-2 vec b=3( vec axx vec b), then find the value of vec c dot vec b

Consider the vectors vec a = hat i + 2 hat j - 3 hat k and vec b = 4 hat i - hat j + 2 hat k . (i) Find |vec a| and |vec b| . (ii) Find vec a. vec b (iii) Find the projections of vec a on vec b and vec b on vec a .

If vec a xx vec b and vec a. vecb = 0 then

If vec a , a n d vec b are unit vectors , then find the greatest value of | vec a+ vec b|+| vec a- vec b|dot

Given three vectors vec a , vec b ,a n d vec c two of which are non-collinear. Further if ( vec a+ vec b) is collinear with vec c ,( vec b+ vec c) is collinear with vec a ,| vec a|=| vec b|=| vec c|=sqrt(2)dot Find the value of vec a . vec b+ vec b . vec c+ vec c . vec a a. 3 b. -3 c. 0 d. cannot be evaluated

Let vec a , vec b , vec c be three unit vectors and vec a . vec b= vec a . vec c=0. If the angel between vec b and vec c is pi/3 , then find the value of |[ vec a vec b vec c]| .