If `|vec(a)| = sqrt(3), |vec(b)| = 2` and angle between `vec(a)` and `vec(b)` is `60^(@)` , find `vec(a).vec(b)`.

If |vec(a)| = 5, |vec(b)| = 6 and the angle between vec(a) and vec(b) is 60^(@) , then vec(a).vec(b) =

If |vec a| =4 , |vec b | = 2 and angle between vec a and vec b is pi/6 , then (vec a xx vec b)^(2) is

If |vec(a)| = 3, |vec(b) = 4 and |vec(a) + vec(b)| = 1 , then |vec(a) - vec(b)| =

If |vec a - vec b| = |vec a| = |vec b| =1 then the angle between vec a and vec b is

If vec(a), vec(b) and vec(c ) are three unit vectors such that vec(a).vec(b) = vec(a).vec(c ) = 0 and angle between vec(b) and vec(c ) is (pi)/(6) , prove that vec(a) = +-2(vec(b) xx vec(c )) .

If vec a. vec b = ~ |vec a||vec b| then angle between vec a and vec b is

If |vec a| = 2, |vec b| = 5 and |vec a xx vec b| = 8 then vec a . vec b

If |vec a| = 4, |vec b| = 2, |vec c| = 6 and each of the angles between the vectors is 60^(o) then |vec a + vec b + vec c| =

If vec(a) and vec(b) are unit vectors, then find the angle between vec(a) and vec(b) , given that (sqrt(3)vec(a) - vec(b)) is a unit vector.