Prove that the vector relation `pveca+qvecb +rvecc+….=0` will be inependent of the orign if and only if `p+q+r+.=0, where p,q,r………` are scalars.

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))

If lines p x+q y+r=0,q x+r y+p=0 and r x+p y+q=0 are concurrent, then prove that p+q+r=0 (where p ,q ,r are distinct ) .

If A,B,C are three points with position vectors veci+vecj,veci-hatj and pveci+qvecj+rveck respectiey then the points are collinear if (A) p=q=r=0 (B) p=qr=1 (C) p=q,r=0 (D) p=1,q=2,r=0

Figure show's three vectors p,q and r where C is the mid - point of AB Then which of the following relation is correct ?

Show that the reflection of the line px+qy+r=0 in the line x+y+1 =0 is the line qx+py+(p+q-r)=0, where p!= -q .

If lines p x+q y+r=0,q x+r y+p=0 and r x+p y+q=0 are concurrent, then prove that p+q+r=0(where, p ,q ,r are distinct )dot

Let veca, vecb and vecc be non - coplanar unit vectors, equally inclined to one another at an angle theta . If veca xx vecb + vecb xx vecc = p veca + q vecb + rvecc , find scalars p, q and r in terms of theta .

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 .

If vec r_1, vec r_2, vec r_3 are the position vectors of the collinear points and scalar p a n d q exist such that vec r_3=p vec r_1+q vec r_2, then show that p+q=1.

P(vec p) and Q(vec q) are the position vectors of two fixed points and R(vec r) is the position vectorvariable point. If R moves such that (vec r-vec p)xx(vec r -vec q)=0 then the locus of R is