If `( vec axx vec b)^2+( vec a dot vec b)^2=144a n d| vec a|=4,` then find the value of `| vec b|dot`

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

If the angel between unit vectors vec aa n d vec b60^0 , 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].

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

If vec a=2 vec i+3 vec j- vec k , vec b=- vec i+2 vec j-4 vec ka n d vec c= vec i+ vec j+ vec k , then find thevalue of ( vec axx vec b)dot( vec axx vec c)dot

If vec a , vec ba n d vec c are three non-zero vectors, no two of which ar collinear, vec a+2 vec b is collinear with vec c and vec b+3 vec c is collinear with vec a , then find the value of | vec a+2 vec b+6 vec c|dot

If vec a , vec b ,a n d vec c are mutually perpendicular vectors and vec a=alpha( vec axx vec b)+beta( vec bxx vec c)+gamma( vec cxx vec a)a n d[ vec a vec b vec c]=1, then find the value of alpha+beta+gammadot

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

If vec aa n d vec b are two vectors and angle between them is theta, then | vec axx vec b|^2+( vec adot vec b)^2=| vec a|^2| vec b|^2 | vec axx vec b|=( vec adot vec b),iftheta=pi//4 vec axx vec b=( vec adot vec b) hat n ,(w h e r e hat n is unit vector, ) if theta=pi//4 ( vec axx vec b)dot( vec a+ vec b)=0

Let vec a , vec ba n d vec c be three non-coplanar vectors and vec p , vec qa n d vec r the vectors defined by the relation vec p=( vec bxx vec c)/([ vec a vec b vec c]), vec q=( vec cxx vec a)/([ vec a vec b vec c])a n d vec r=( vec axx vec b)/([ vec a vec b vec c])dot Then the value of the expression ( vec a+ vec b)dot vec p+( vec b+ vec c)dot vec q+( vec c+ vec a)dot vec r is a. 0 b. 1 c. 2 d. 3