Last updated at Dec. 8, 2016 by Teachoo

Transcript

Ex10.1, 11 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. Let m1 & m2 be the slopes of two lines We know that angles between two lines are tan θ = |(𝑚2 − 𝑚1)/(1 + 𝑚1𝑚2)| Here tan θ = 1/3 & m2 = 2m1 Putting values tan θ = |(𝑚2 − 𝑚1)/(1 + 𝑚1𝑚2)| 1/3 = |(𝑚2 − 𝑚1)/(1 + 𝑚1𝑚2)| 1/3 = |(2𝑚1 − 𝑚1)/(1 + 𝑚1(2𝑚1))| 1/3 = |𝑚_1/(1 + 2〖𝑚_1〗^2 )| |𝑚_1/(1 + 2〖𝑚_1〗^2 )| = 1/3 So, 𝑚_1/(1 + 2〖𝑚_1〗^2 ) = 1/3 or 𝑚_1/(1 + 2〖𝑚_1〗^2 ) = ( −1)/3 Hence slope of lines are 1/2 and 1 or 1 and 2 or ( − 1)/2 and -1 or -1 and -2

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