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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