Angle between the lines xa+yb=1andxa-yb=1is
2tan-1(ba)
tan-1(2aba2-b2)
tan-1(a2-b2a2+b2)
Noneofthese
Finding the angle :
Given,
xa+yb=1...(i)&xa-yb=1...(ii)
Equation (i) can be written as
y=-bax+1 where slope m1=-ba
Equation (ii) can be written as
y=bax+1where slope m2=ba
Now angle between line (i) & (ii) is
tanθ=|m1+m21-m1.m2|=-ba-ba1-b2a2tanθ=-2baa2-b2a2=-2aba2-b2=-2ab-b2+a2θ=tan-1-2ab-b2+a2
Therefore, angle between (i) & (ii) is θ=tan-1-2ab-b2+a2
Hence, correct option is (B)
Solve the following system of linear equations forxandy
xa+yb=2;bx-ay=a+b
A plane P intersects lines L1, L2, L3 and L4 at A, B, C, D L1:x−32=y−31=z−32 L2:x−32=y−31=z2L3:x2=y−31=z2 L4:x2=y−31=z−32 then the minimum area of quadrilateral ABCD is ___.
Evaluate the following expression forx=-1,y=-2,z=3
xy+yz+zx