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 m_{1} and m be the slope of the two given lines such that m_{1}= 2m

We know that if θ is the angle between the lines l1 and l2 with slope m_{1} and m_{2}, then

Given here that the tangent of the angle between the two lines is

∴

⇒

Case 1

⇒

⇒ 1+2m^{2} = -3m

⇒ 2m^{2} +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

⇒

⇒ 2m^{2} +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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