Question

show that the lines 3x-2y+6 =0.. and 2x+ 3y -1=0 are perpendicular to each oher​

Answer 1

Answer:

first line function is y=f(x)=(3x/2 + 1)

and f(x+dx)=3((x+dx+2)/2)

N1 = Slope of the first line as Rate of change in f(x) to change in x:

N1 = (f(x+dx)-f(x))/dx = 3/2

second line function is y=f(x)=(1-2x)/3

and f(x+dx)=(1-2(x+dx))/3

N2 = Slope of the second line as Rate of change in f(x) to change in x:

N2 = (f(x+dx)-f(x))/dx = -2/3

so:

N1 . N2= -1

then :

the two lines are perpendicular to each other