If the points `(p ,\ q),\ (m ,\ n)` and `(p-m ,\ q-n)` are collinear, show that `p n=q m` .

If the points (p,q),(m,n) and (p-m,q-n) are collinear,show that pn=qm.

If A (p , q) , B (m , n) and C ( p - m , q - n ) are collinear then pn = ......

In triangle P Q R , if P Q=R Q\ a n d\ L ,\ M\ a n d\ N are the mid-points of the sides P Q ,\ Q R\ a n d\ R P respectively. Prove that L N=M N .

In A P Q R , if P Q=QR\ a n d\ L ,\ M\ a n d\ N are the mid-points of the sides P Q ,\ P R\ a n d\ R P respectively. Prove that L N=M N

Consider the following relations: R = {(x, y) | x, y are real numbers and x = wy for some rational number w}; S={(m/n , p/q)"m , n , p and q are integers such that n ,q"!="0 and q m = p n"} . then,

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 p^(th), q^(th) and r^(th) terms of an A. P. are l, m, n, respectively, show that (q - r )l + (r -p)m +(p - q)n =0

If pth, qth and rth terms of an A.P. are l, m, n respectively, show that (q-r)l+(r-p)m+(p-q)n=0

If the (m + n)th and (m - n)th term of a G.P. are p and q respectively, then the mth term is …….. .

In a G.P., the (p + q)th term is m and (p-q)th term is n. Find its pth term.