The Total solution for NCERT class 6-12
Show that the diagonals of the parallelogram whose sides are lx + my + n= 0, lx + my + n’ = 0, mx + ly + n = 0 and mx + ly + n’ = 0 include an angleπ/2.
Given:
The given lines are
lx + my + n = 0 … (1)
mx + ly + n’ = 0 … (2)
lx + my + n’ = 0 … (3)
mx + ly + n = 0 … (4)
Let us prove, the diagonalsof the parallelogram whose sides are lx + my + n = 0, lx + my + n’ = 0, mx + ly+ n = 0 and mx + ly + n’ = 0 include an angle π/2.
By solving (1) and(2), we get
∴ m1m2 =-1
Hence proved.