Prove that `Prarr q equiv~q rarr~p`

l and m are two parallel line intersects by another point of parallel lines p and q show that triangle ABC equiv triangleCDA

At what angles do the two fores (overset rarr P + overset rarr Q ) adn (overst rarr P - overset rarr Q) act so that the agnitude of the resultantts is sqrt(2(P^2 + Q^2 ) ) ?

Three vectors overset rarr P,overset rarr Q and overset rarr R satisfy the relations overset rarr P cdot overset rarr Q = 0 and overset rarr P * overset rarr R = 0 .To which vector, the vector overset rarr P is parallel to .

If the magnitude of vectors overset rarr P,overset rarr Q and oversert rarr R are 3,4 and 5 units respectively,and if overset rarr P + overset rarr Q = overset rarr R ,then what will be the angle between overset rarr P and overset rarr R ?

Prove that the equation p cos x - q sin x =r admits solution for x only if -sqrt(p^(2)+q^(2)) lt r lt sqrt(p^(2)+q^(2))

Sum of first p,q and r terms of an A.P. are a,b,c respectively. Prove that a/p(q-r) +b/q(r-p) + c/r(p-q)=0 .

If p ,q, r are in A.P., a is G.M. between p, q and b is G.M. between q, r, then prove that a^2, q^2, b^2 are in A.P.

ABCD is a parallelogram. The circle through A,B is so drawn that it intersects AD at P and CB at Q. Prove that P,Q,C and D are concyclic.

If agt0,bgt0,cgt0 be respectively the pth, qth and rth terms of a G.P. are a, b ,c , prove that : (q-r) log a+ (r -p) log b + (p -q) log c = 0 .

Sum of the first p, q and r terms of an A.P. are a, b and c, respectively. Prove that a/p(q-r)+b/q(r-p)+c/r(p-q)=0