Let ` vec aa n d vec b` be unit vectors such that `| vec a+ vec b|=sqrt(3)` . Then find the value of `(2 vec a+5 vec b)dot(3 vec a+ vec b+ vec axx 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].

Show that ( vec a- vec b)xx( vec a+ vec b)=2( vec axx vec b)dot

If [ vec a vec b vec c]=2, then find the value of [( vec a+2 vec b- vec c)( vec a- vec b)( vec a- vec b- vec c)]dot

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

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 the angel between unit vectors vec aa n d vec b60^0 , then find the value of | vec a- vec b|dot

Let vec aa n d vec b be unit vectors that are perpendicular to each other. Then [ vec a+( vec axx vec b) vec b+( vec axx vec b) vec axx vec b] will always be equal to a. 1 b. 0 c. -1 d. none of these

If vec a and vec b be two unit vectors such that vec a+ vec b is also a unit vector, then find the angle between vec a and vec b

If vec aa n d vec b are two vectors, then prove that ( vec axx vec b)^2=| vec adot vec a vec adot vec b vec bdot vec a vec bdot vec b| .

If aa n db are vectors in space given by vec a=( hat i-2 hat j)/(sqrt(5))a n d vec b=( hat2i+ hat j+3 hat k)/(sqrt(14)) , then find the value of (2 vec a+ vec b)dot[( vec axx vec b)xx( vec a-2 vec b)]dot