In ` triangle A B C ,` a point `P` is taken on `A B` such that `A P//B P=1//3` and point `Q` is taken on `B C` such that `C Q//B Q=3//1` . If `R` is the point of intersection of the lines `A Qa n dC P ,` using vector method, find the area of ` A B C` if the area of ` B R C` is 1 unit

In a triangle A B C ,Da n dE are points on B Ca n dA C , respectivley, such that B D=2D Ca n dA E=3E Cdot Let P be the point of intersection of A Da n dB Edot Find B P//P E using the vector method.

Let the base A B of a triangle A B C be fixed and the vertex C lies on a fixed circle of radius rdot Lines through Aa n dB are drawn to intersect C Ba n dC A , respectively, at Ea n dF such that C E: E B=1:2a n dC F : F A=1:2 . If the point of intersection P of these lines lies on the median through A B for all positions of A B , then the locus of P is (a) a circle of radius r/2 (b) a circle of radius 2r (c) a parabola of latus rectum 4r (d) a rectangular hyperbola

O P Q R is a square and M ,N are the middle points of the sides P Qa n dQ R , respectively. Then the ratio of the area of the square to that of triangle O M N is 4:1 (b) 2:1 (c) 8:3 (d) 7:3

The points A and B trisect the line -segment joining the points P(2,1-3) and Q(5,-8,3) , find the coordinates of the points A and B.

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 find the mid-point of P and R

The tangent at any point P to a curve C intersects the coordinate axes at A and B. If P be the mid-point of the line segment AB and the curve passes through the point (1,1), find the equation of the curve C.

Points A, B, C lie on the parabola y^2=4ax The tangents to the parabola at A, B and C, taken in pair, intersect at points P, Q and R. Determine the ratio of the areas of the triangle ABC and triangle PQR

A B C is a triangle, P is a point on A B a n dQ is a point on A C such that /_A Q P=/_A B Cdot Complete the relation (A r e aof A P Q)/(A r e aof A B C)=dot(())/(A C^2) .

If (2 , -3 , 1) is the centroid of the triangle ABC with vertices A (-3 , p , 2) , B (2 , -4 , q) and C (r , 3 , 5) , find the values of p , q , r .

If the points P (a, 1), Q (1, b), R (-2, 11) are collinear and Q be the mid - point of bar(PR) , then find the value of a and b.