A straight line L through the origin meets the lines `x + y = 1` and `x + y = 3` at P and Q respectively. Through P and Q two straight lines `L_1`, and` L_2` are drawn, parallel to `2x-y- 5` and `3x +y 5` respectively. Lines `L_1` and `L_2` intersect at R. Locus of R, as L varies, is

A straight line L through the origin meets the lines x + y = 1 and x + y = 3 at P and Q respectively. Through P and Q two Straight lines L_1 and L_2 are drawn parallel to 2x- y=5 and 3x+y=5 respectively. Lines L_1 and L_2 intersect at R. Show that the locus of R, as L varies, is a straight line.

A straight lines L through the origin meets the lines x+y=1 and x+y=3 at P and Q respectively. Through P and Q two straight lines L_1 and L_2 are drawn, parallel to 2x-y=5 and 3x+y=5 respectively. Line L_1 and L_2 intersect at R. Show that the locus of R as L varies is a straight line.

A straight-line L through the origin meets the lines x+y=1 and x+y=3 at P and Q respectively. Through P and Q two straight lines L_(1) and L_(2) are drawn, parallel to 2x-y=5 and 3x+y=5 , respectively. Lines L_(1) and L_(2) intersect at R, show that the locus of R as L varies, is a straight line

A straight line L through the origin meet the lines x+y=1 and x+y=3 at P and Q, respectively. Lines L_1 and L_2 " are drawn , parallel to 2x-y=5 and 3x=y=5 respectively lines " L_1 and L_2 intersect at R.Then that the locus of R, as L varies, is a staright line.

A straight line L passing through the point P(-2,-3) cuts the lines, x + 3y = 9 and x+y+1=0 at Q and R respectively. If (PQ) (PR) = 20 then the slope line L can be (A) 4 (B) 1 (C) 2 (D) 3

A line L passing through (1, 1) intersect lines L_1: 12 x+5y=13 and L_2: 12 x+5y=65 at A and B respectively. If A B=5 , then line L can be

A line L passing through (1, 1) intersect lines L_1: 12 x+5y=13 and L_2: 12 x+5y=65 at A and B respectively. If A B=5 , then line L can be

A line L passes through the point P(5,-6,7) and is parallel to the planes x+y+z=1 and 2x-y-2z=3 .What is the equation of the line L ?

Let a line L_(1):3x+2y-6=0 intersect the x and y axes at P and Q respectively.Let another line L_(2) perpendicular to L_(1) cut the x and y axes at R and S respectively.The locus of point of intersection of the lines PS and QR is

A variable line L is drawn through O(0, 0) to meet lines L1: 2x + 3y = 5 and L2: 2x + 3y = 10 at point P and Q, respectively. A point R is taken on L such that 2OP.OQ = OR.OP + OR.OQ. Locus of R is