Question

The acute angle between the lines x – 3y – 6 = 0 and y = 2x + 5 is

Answer 1

Explanation:

eq. of line x-3y-6=0

3y=x-6

y=1/3 x-6/3

or

y=1/3 x-2

its slope m1=1/3

y=2x+5

slope m2=2

if α is the angle between the lines then

`tan~\alpha =|(m1-m2)/(1+m1m2) |=|((1)/(3) -2)/(1+1/3* 2)| =|(1-3*2)/(3+2)| =5/5=1=tan 45\\\alpha =45^\circ\\`