If ` vec P O+ vec O Q= vec Q O+ vec O R ,` show that the point, `P ,Q ,R` are collinear.

If vec PO+vec OQ=vec QO+vec OR, show that the point,P,Q,R are collinear.

if vec(P) xx vec(R ) = vec(Q) xx vec(R ) , then

Let O be the origin and let PQR be an arbitrary triangle. The point S is such that vec O Pdot vec O Q+ vec O Rdot vec O S= vec O Rdot vec O P+ vec O Qdot vec O S= vec O Q . vec O R+ vec O Pdot vec O S Then the triangle PQ has S as its: circumcentre (b) orthocentre (c) incentre (d) centroid

If vec p xxvec q = vec m xxvec n and vec p xxvec m = vec q xxvec n show that vec p-vec n is parallel to vec q-vec m where vec p! = Vec n and vec q! = Vec m

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

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

Let vec OA=vec a,vec OB=100vec a+2vec b and vec OC=vec b where O,A,C are non collinear points.Let P denotes the area of the parallelogram with vec O Anad vec OC as adjacent sides and Q denotes the area of the quadrilateral OABC If Q=lambda P Find the value of lambda

Let OP,OQ, OR are three edges of a regular tetrahedron of edge length a . If vec p , vec q and vec r are the position vectors of the points P,Q and R & O is the origin then |vec p timesvec q+vec q timesvec r+vec r timesvec p| is equal to

If vec P+ vec Q = vec R and |vec P| = |vec Q| = | vec R| , then angle between vec P and vec Q is