If `lx + my + n = 0`, where `l, m, n` are variables, is the equation of a variable line and `l, m, n` are connected by the relation `al+bm+cn=0` where `a, b, c` are constants. Show that the line passes through a fixed point.

Find the direction cosines of the lines, connected by the relations: l+m+n=0 and 2l m+2ln-m n=0.

Find the direction cosines of the lines, connected by the relations: l+m+n=0 and 2l m+2ln-m n=0.

The direction cosines l, m and n of two lines are connected by the relations l+m+n=0 and lm=0 , then the angle between the lines is

Find the angle between the lines whose direction cosines are connected by the relations l+m+n=0a n d2lm+2n l-m n=0.

Find the direction cosines of the two lines which are connected by th relations. l-5m+3n=0 and 7l^2+5m^2-3n^2=0

Find the angle between the lines whose direction cosines are connected by the relations l+m+n=0a n d2//m+2n l-m n=0.

The direction cosines of two lines are connected by relation l+m+n=0 and 4l is the harmonic mean between m and n. Then,

If the algebraic sum of perpendiculars from n given points on a variable straight line is zero then prove that the variable straight line passes through a fixed point

Let a x+b y+c=0 be a variable straight line, whre a , ba n dc are the 1st, 3rd, and 7th terms of an increasing AP, respectively. Then prove that the variable straight line always passes through a fixed point. Find that point.

Let a x+b y+c=0 be a variable straight line, whre a , ba n dc are the 1st, 3rd, and 7th terms of an increasing AP, respectively. Then prove that the variable straight line always passes through a fixed point. Find that point.