` vec a , vec b ,a n d vec c` are three unit vectors and every two are inclined to each other at an angel `cos^(-1)(3//5)dot` If ` vec axx vec b=p vec a+q vec b+r vec c ,w h e r ep ,q ,r` are scalars, then find the value of `qdot`

Let vec a,vec b, and vec c be non-coplanar unit vectors,equally inclined to one another at an angle theta. If vec a xxvec b+vec b xxvec c=pvec a+qvec b+rvec c, find scalars p,q and r in terms of theta .

If vec p xxvec q=vec r and vec p*vec q=c, then vec q is

Let vec a,vec b, and vec c be three non coplanar unit vectors such that the angle between every pair of them is (pi)/(3). If vec a xxvec b+vec b .If where p ,q, r are scalars then the value of (p^(2)+2q^(2)+r^(2))/(q^(2)) is

Let vec a,vec b,vec c and are unit vectors inclined to each otherat an angle of (2 pi)/(3). If hat p,hat q and hat r are unit vectors alongthe angle bisectors of vec a and vec b,vec b and vec c and vec a are spectively, then [hat phat qhat r] is equal to

Statement 1: vec a , vec b ,a n d vec c are three mutually perpendicular unit vectors and vec d is a vector such that vec a , vec b , vec ca n d vec d are non-coplanar. If [ vec d vec b vec c]=[ vec d vec a vec b]=[ vec d vec c vec a]=1,t h e n vec d= vec a+ vec b+ vec c Statement 2: [ vec d vec b vec c]=[ vec d vec a vec b]=[ vec d vec c vec a] =>vec d is equally inclined to veca,vecb,vecc.

prove that | vec axx vec b|=( vec adot vec b)t a ntheta, w h e r e theta is the angle between vec a a n d vec bdot

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 avec bvec c]|

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

vec a,vec b and vec c are three non-coplanar vectors and vec r is any arbitrary vector.Prove that [vec bvec cvec r]vec a+[vec c+vec avec r]vec b+[vec avec bvec r]vec c=[vec avec bvec c]vec r

Let vec a* vec b=0,w h e r e vec aa n d vec b are unit vectors and the unit vector vec c is inclined at an angle theta to both vec aa n d vec bdot If vec c=m vec a+n vec b+p( vec axx vec b),(m ,n , p in R), then a.pi/4lt=thetalt=pi/4 b. pi/4lt=thetalt=(3pi)/4 c. 0lt=thetalt=pi/4 d. 0lt=thetalt=(3pi)/4