Question Number 39899 by Rio Mike last updated on 13/Jul/18
![Given the lines l_1 ; 3y = 2x ,l_2 ; y = −((3x)/2) + p and l_3 ; y ^ = x + 1 a) find the value of p if the point of intersection between l_1 and l_2 is (3,5) b) find the cosine of the angle between l_2 and l_3 c) which line holds the point (1,2). d)find the line l_4 with gradient ∫_4 ^π [l_1 + l_2 dx] perpendicur to l_2 ,parrallel to l_1 .](Q39899.png)
$${Given}\:{the}\:{lines}\: \\ $$$${l}_{\mathrm{1}} ;\:\mathrm{3}{y}\:=\:\mathrm{2}{x}\:,{l}_{\mathrm{2}} ;\:{y}\:=\:−\frac{\mathrm{3}{x}}{\mathrm{2}}\:+\:{p} \\ $$$${and}\:{l}_{\mathrm{3}} ;\:{y}\overset{} {\:}=\:{x}\:+\:\mathrm{1} \\ $$$$\left.{a}\right)\:{find}\:{the}\:{value}\:{of}\:{p}\:{if}\: \\ $$$${the}\:{point}\:{of}\:{intersection}\:{between} \\ $$$${l}_{\mathrm{1}} \:{and}\:{l}_{\mathrm{2}} \:{is}\:\left(\mathrm{3},\mathrm{5}\right) \\ $$$$\left.{b}\right)\:{find}\:{the}\:{cosine}\:{of}\:{the}\:{angle} \\ $$$${between}\:{l}_{\mathrm{2}} \:{and}\:{l}_{\mathrm{3}} \\ $$$$\left.{c}\right)\:{which}\:{line}\:{holds}\:{the}\:{point} \\ $$$$\left(\mathrm{1},\mathrm{2}\right). \\ $$$$\left.{d}\right){find}\:{the}\:{line}\:{l}_{\mathrm{4}} \:{with}\:{gradient} \\ $$$$\int_{\mathrm{4}} ^{\pi} \left[{l}_{\mathrm{1}} \:+\:{l}_{\mathrm{2}} \:{dx}\right]\:{perpendicur}\:{to} \\ $$$${l}_{\mathrm{2}} ,{parrallel}\:{to}\:{l}_{\mathrm{1}} . \\ $$