If ` vec a` and ` vec b` are non-collinear vectors and ` vec A=(p+4q) vec a=(2p+q+1) vec b a n d vec B=(-2p+q+2) vec a+(2p-3q-1) vec b` ,a n d if`3 vec A=2 vec B` , then determine p and q.

Vectors vec a and vec b are non-collinear.Find for what value of n vectors vec c=(n-2)vec a+vec b and vec d=(2n+1)vec a-vec b are collinear?

If vec P and vec Q are two vectors, then the value of (vec P + vec Q) xx (vec P - vec Q) is

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

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

If vec p = vec a + vec b, vec q = vec a-vec b | vec a | = | vec b | = 1 then | vec p xxvec q | =

For three vectors vec p,vec q and vec r if vec r=3vec p+4vec q and 2vec r=vec p-3vec q then

If vec a,vec b,vec c be any three non-zero non coplanar vectors and vectors vec p=(vec b xx vec c)/(vec a.vec b xx vec c),vec q=(vec c xx vec a)/(vec a.vec b xx vec c) vec r=(vec a xx vec b)/(veca.vec b xx vec c), then [vec p vec q vec r] equals -

If vec a, vec b, vec c are three non-coplanar vectors and vec p, vec q, vec r are vectors defined by the relations vec p = (vec b xxvec c) / ([vec avec bvec c]), vec q = (vec c xxvec a) / ([vec avec bvec c]), vec r = (vec a xxvec b) / ([vec avec bvec c]) then the value of expression (vec a + vec b) * vec p + (vec b + vec c) * vec q + (vec c + vec a) * vec r is equal to

Vectors vec Aa n d vec B satisfying the vector equation vec A+ vec B= vec a , vec Axx vec B= vec ba n d vec A*vec a=1,w h e r e vec aa n d vec b are given vectors, are a. vec A=(( vec axx vec b)- vec a)/(a^2) b. vec B=(( vec bxx vec a)+ vec a(a^2-1))/(a^2) c. vec A=(( vec axx vec b)+ vec a)/(a^2) d. vec B=(( vec bxx vec a)- vec a(a^2-1))/(a^2)

Find the angle between the vectors vec a = 2 vec p + 4 vec q and vec b = vec p- vec q where vec p and vec q are unit vectors forming an angle of 120^@ .