Q. 154.2( 9 Votes )
The slope of a line is double of the slope of another line. If tangent of the angle between them is 1/3, find the slopes of the lines.
Answer :
let m1 and m be the slope of the two given lines such that m1= 2m
We know that if θ is the angle between the lines l1 and l2 with slope m1 and m2, then
Given here that the tangent of the angle between the two lines is 
∴ 
⇒ 
Case 1
⇒ 
⇒ 1+2m2 = -3m
⇒ 2m2 +1 +3m = 0
⇒2m(m+1) + 1(m+1)=0
⇒(2m+1)(m+1)= 0
⇒ m =-1 or 
If m = -1, then the slope of the lines are -1 and -2
If m = 
, then the slope of the lines are 
and -1
Case 2
⇒
⇒ 2m2 +1 -3m = 0
⇒ m = 1 or 1/2
If m = 1, then the slope of the lines are 1 and 2
If m = 
, then the slope of the lines are 
and 1
Hence the slope of the lines are -1 and -2 or 
and -1 or 1 and 2 or 
and 1.
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