If ` vec b` is not perpendicular to ` vec c ,` then find the vector ` vec r` satisfying the equation ` vec rxx vec b= vec axx vec b` and `vec r. vec c=0.`

If vec a and vec b are two given vectors and k is any scalar, then find the vector vec r satisfying vec rxx vec a+k vec r= vec b .

If vec a_|_ vec b , then vector vec v in terms of vec aa n d vec b satisfying the equation s vec vdot vec a=0a n d vec vdot vec b=1a n d[ vec v vec a vec b]=1 is a. vec b/(| vec b|^2)+( vec axx vec b)/(| vec axx vec b|^2) b. vec b/(| vec b|^)+( vec axx vec b)/(| vec axx vec b|^2) c. vec b/(| vec b|^2)+( vec axx vec b)/(| vec axx vec b|^) d. none of these

If c is a given non-zero scalar, and vec A and vec(B) are given non-zero vector such that vec A_|_ vecB , then find vector vec X which satisfies the equation vec A . vec X =c and vec Axx vec X= vec Bdot

If vec a+ vec b+ vec c = vec 0 then prove that vec axx vec b= vec bxx vec c = vec cxxvec a .

Let vec A=2 vec i+ vec k , vec B= vec i+ vec j+ vec kdot vec C = 4hati-3hatj+7hatk Determine a vector vec R satisfying vec Rxx vec B= vec Cxx vec B and vec R. vec A=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

Let vec a= hat i+ hat j ; vec b=2 hat i- hat kdot Then vector vec r satisfying vec rxx vec a= vec bxx vec a and vec rxx vec b= vec axx vec b then vecr is a. hat i- hat j+ hat k b. 3 hat i- hat j+ hat k c. 3 hat i+ hat j- hat k d. hat i- hat j- hat k

If vec axx( vec bxx vec c) is perpendicular to ( vec axx vec b)xx vec c , we may have a. ( vec a. vec c)| vec b|^2=( vec a. vec b)( vec b.vec c)( vec c.vec a) b. vec adot vec b=0 c. vec adot vec c=0 d. vec bdot vec c=0

Let vec r be a unit vector satisfying vec rxx vec a= vec b ,w h e r e| vec a|=sqrt3a n d| vec b|=sqrt2. Then vec r =?

The equation of a line passing through the point vec a parallel to the plane vec r. vec n=q and perpendicular to the line vec r= vec b+t vec c is a. vec r= vec a+lambda( vec nxx vec c) b. ( vec r- vec a)xx( vec nxx vec c) c. vec r= vec b+lambda( vec nxx vec c) d. none of these