Question

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 slope of the line.​

Answer 1

Answer:

your solution is as follows

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Step-by-step explanation:

$to \: find : \\ slope \: of \: lines \: (m1 \: and \: m2) \\ \\ so \: let \: here \\ slopes \: of \: required \: two \: lines \: be \\ m1 \: and \: m2 \\ \\ according \: to \: first \: condition \\ m1 = 2.m2 \: \: \: \: \: \: \: \: \: (1) \\ \\ we \: know \: that \\ tangent \: angle \: between \: two \: slopes \\ is \: given \: by \\ \\ tan \: x = | \frac{m1 - m2}{1 + m1.m2} \: | \\ \\ according \: to \: second \: condition \\ \frac{1}{3} = | \frac{m1 - m2}{1 + m1.m2} | \\ \\ = | \frac{2m2 - m2}{1 + 2m2.m2} \: | \\ \\ \frac{1}{3} = | \frac{m2}{1 + 2.m2 {}^{2} } | \\ \\ 1 + 2.m2 {}^{2} = 3m2 \\ 2m {2}^{2} - 3m2 + 1 = 0 \\ \\ 2m {2}^{2} - 2m2 - m2 + 1 = 0 \\ 2m2(m2 - 1) - 1(m2 - 1) = 0 \\ \\ (2m2 - 1)(m2 - 1) = 0 \\ m2 = 1 \: \: or \: \: m2 = \frac{1}{2}$

$substitute \: values \: of \: m2 \: in \: (1) \\ we \: get \\ m1 = 1 \: \: or \: \: m1 = 2$