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.

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 if3 vec A=2 vec B , then determine p and q.

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

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^@ .

If vec r=3vec p+4vec q and 2vec r=vec p-3vec q then

vec a , vec b , vec c are three coplanar unit vectors such that vec a+ vec b+ vec c=0. If three vectors vec p , vec q ,a n d vec r are parallel to vec a , vec b ,a n d vec c , respectively, and have integral but different magnitudes, then among the following options, | vec p+ vec q+ vec r| can take a value equal to a. 1 b. 0 c. sqrt(3) d. 2

vec a , vec b , vec c are three coplanar unit vectors such that vec a+ vec b+ vec c=0. If three vectors vec p , vec q ,a n d vec r are parallel to vec a , vec b ,a n d vec c , respectively, and have integral but different magnitudes, then among the following options, | vec p+ vec q+ vec r| can take a value equal to a. 1 b. 0 c. sqrt(3) d. 2

vec a , vec b , vec c are three coplanar unit vectors such that vec a+ vec b+ vec c=0. If three vectors vec p , vec q ,a n d vec r are parallel to vec a , vec b ,a n d vec c , respectively, and have integral but different magnitudes, then among the following options, | vec p+ vec q+ vec r| can take a value equal to a. 1 b. 0 c. sqrt(3) d. 2

If P ,Q and R are three collinear points such that vec P Q= vec a and vec Q R = vec bdot Find the vector vec P R .