3-2 (a + b + +EXAMPLE 6 Show that the following lines are concurrentL1 = (a - b) x + ( -c) y + (0-) = 0L2 = (b -c) x + (-a) y + (a - b) = 0inter and, L3 = (c - a) x + (a - b) y + (6 - 2) = 0.SOLUTION Clearly,

L_1=(a-b)x+(b-c)y+(c-a)=0L_2=(b-c)x+(c-a)y+(a-b)=0L_3=(c-a)x+(a-b)y+(b-c)=0 KAMPLE 6 Show that the following lines are concurrent L1 = (a-b) x + (b-c)y + (c-a) = 0 12 = (b-c)x + (c-a) y + (a-b) = 0 L3 = (c-a)x + (a-b) y + (b-c) = 0. ,

Show that the following lines are concurrent: L_1=(a-b)x+(b-c)y+(c-a)=0 L_2=(b-c)x+(c-a)y+(a-b)=0 L_3=(c-a)x+(a-b)y+(b-c)=0

Show that the following lines are concurrent: L_(1)=(a-b)x+(b-c)y+(c-a)=0L_(2)=(b-c)x+(c-a)y+(a-b)=0L_(3)=(c-a)x+(a-b)y+(b-c)=0

Show that the following system is inconsistent. (a-b)x+(b-c)y+(c-a)z=0 (b-c)x+(c-a)y+(a-b)z=0 (c-a)x+(a-b)y+(b-c)z=1

Show that two lines a_(1) x + b_(14) y + c_(1) = 0 and a_(2) x + b_(2) y + c_(2) = 0 , where b_(1) , b_(2) ne 0 are Perpendicular if a_(1) a_(2) + b_(1) b_(2) =0 .

Show that the straight lines L_1=(b+c)x+a y+1=0,\ L_2=(c+a)x+b y+1=0\ n d\ L_3=(a+b)x+c y+1=0\ are concurrent.

If the line a x+b y+c=0 is a normal to the curve x y=1, then (a) a >0,b >0 (b) a >0,b >0 (d) a 0

Prove that the lines (b-c)x+(c-a)y+(a-b)=0, (c-a)x+(a-b)y+(b-c)=0 and (a-b)x+(b-c)y+(c-a)=0 are concurrent.