the diagonals of the parallelogram formed by the the lines `a_1x+b_1y+c_1=0 ,a_1x+b_1y+c_1 '=0 , a_2x+b_2y+c_1=0 , a_2x+b_2y+c_1 '=0` will be right angles if:

the diagonals of the parallelogram formed by the the lines a_(1)x+b_(1)y+c_(1)=0,a_(1)x+b_(1)y+c_(1)^(prime)=0,a_(2)x+b_(2)y+c_(1)=0,a_(2)x+b_(2)y+c_(1)^(prime) will be right angles if:

Prove that the diagonals of the parallelogram formed by the lines x/a +y/b=1,x/b+y/a= 1, x/a + y/b = 2 and x/b + y/a = 2 are at right angles . Also find its area (a != b)

The angle between the lines a _(1) x + b_(1)y+c_(1) =0 and a _(2)x+ b_(2)y+c_(2)=o, is

Prove that the diagonals of the parallelogram formed by the four lines : (x)/(a)+(y)/(b)=1 , (x)/(a)+(y)/(b)=-1 , (x)/(a)-(y)/(b)=1 , (x)/(a)-(y)/(b)=-1 are at right angles.

Find the equation of the plane whch passes through the line a_1x+b_1y+c_1y+c_1z+d_1=0 a_2x+b_2y+c_2z+d_2=0 and which is parallel to the line (x-alpha)/l=(y-beta)/m=(z-gamma)/n