`P` and `Q` are points on the line joining `A(-2,5)` and `B(3,1)` such that `A P=P Q=Q B` . Then, the distance of the midpoint of `P Q` from the origin is (a)`3 `(b) `(sqrt(37))/2` (c) `4` (d) `3.5`

Let P and Q be point on the line joining A(5,6) and B (3, -4) such that AP=PQ=QB. Then the midpoint of PQ is

Find the position vector of the midpoint of the vector joining the points P(2, 3, 4) and Q(4, 1 -2)

P is a point on the line y+2x=1, and Q and R two points on the line 3y+6x=6 such that triangle P Q R is an equilateral triangle. The length of the side of the triangle is (a) 2/(sqrt(5)) (b) 3/(sqrt(5)) (c) 4/(sqrt(5)) (d) none of these

The image of P(a ,b) on the line y=-x is Q and the image of Q on the line y=x is R . Then the midpoint of P R is (a) (a+b ,b+a) (b) ((a+b)/2,(b+2)/2) (c) (a-b ,b-a) (d) (0,0)

Let O(0,0),P(3,4), and Q(6,0) be the vertices of triangle O P Q . The point R inside the triangle O P Q is such that the triangles O P R ,P Q R ,O Q R are of equal area. The coordinates of R are (a) (4/3,3) (b) (3,2/3) (c) (3,4/3) (d) (4/3,2/3)

If P(x ,y ,z) is a point on the line segment joining Q(2,2,4)a n d R(3,5,6) such that the projections of vec O P on the axes are 13/5, 19/5 and 26/5, respectively, then find the ratio in which P divides Q Rdot

At what angle do the two forces (P+Q) and (P-Q) act so that the resultant is sqrt(3P^(2)+Q^(2)) ?

P and Q are points on the ellipse x^2/a^2+y^2/b^2 =1 whose center is C . The eccentric angles of P and Q differ by a right angle. If /_PCQ minimum, the eccentric angle of P can be (A) pi/6 (B) pi/4 (C) pi/3 (D) pi/12

Find the vector joining the points P(2, 3, 0) and Q(-1, -2, -4) directed from P to Q