Question

Find the angle between the lines x + 2y = 5 and 3x + y = 11

Answer 1

Answer:

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Step-by-step explanation:

$so \: here \\ given \: equations \: are \: \\ x + 2y = 5 \: \: and \: \: 3x + y = 11 \\ \\ so \: comparing \: these \: equations \: with \: \\ a1x + b1y = c1 \: \: and \: \: a2x + b2y = c2 \\ we \: get \\ \\ a1 = 1 \: , \: b1 = 2 \\ a2 = 3 \: , \: b2 = 1 \\ \\ so \: we \: know \: that \\ slope = \frac{ - a}{b} \\ \\ hence \: then \\ \\ m1 = \frac{ - a1}{b1} \\ \\ m1 = \frac{ - 1}{2} \\ \\ similarly \\ \\ m2 = \frac{ - a2}{b2} \\ \\ m2= \frac{ -3 }{1} = - 3$

$so \: now \: we \: know \: that \\ tan \: θ = | \: \frac{m1 - m2}{1 + m1.m2} \: | \\ \\ = | \frac{ \frac{ - 1}{2} - ( - 3)}{1 + \frac{ - 1}{2} \times ( - 3)} | \\ \\ = | \frac{ \frac{ - 1}{2} + 3 }{1 + \frac{3}{2} } | \\ \\ = | \: \frac{ \frac{ - 1 + 6}{2} }{ \frac{2 + 3}{2} } \: | \\ \\ = | \frac{ \frac{ \frac{5}{2} }{5} }{2} | \\ \\ = |1| \\ \\ = 1 \\ we \: know \: that \\ tan \: θ = 45 \\ \\ hence \: then \\ \: θ = 45$