Question

In this problem, let li be the line that passes through the points A(1,2, 4) and B(-1,3,8), and let l2 be the line with symmetric equations x +1 = 2y = 32 — 3. Parts (e) and (f) relate to the vector field F = (xy, xz, yz). (a) Show that the lines li and l2 intersect. (b) Let P be the plane that contains both lines li and lz. Find an equation for P. (c) Show that the points C(61, 35, 31) and D(63, 34, 27) also lie on P. (d) Let R be the quadrilateral whose vertices are ABCD. Show that R is a rectangle. (Hint: by part (c) it is a planar quadrilateral; what are its angles?) (e) What is the flux of F through R in the upwards direction?

Answer 1

(Q AC1,2,4) B(-1,3,3) liaa posses threugi tr point. 아. (-), 2-3, 4 - 3 > - 2 , 1, - 기 A = 1, 2, + > + t 기 2, 1, -4 X +1 = 24 - 32-3 찢 - 뜻 - 2. 쟁블 < Z1 T ! 5 2 1 뗄 는 덜한 tty 야3월 +2월 1, = -1, 1 > + t, G, 3, 2 > l, = l, point at any point o find the intersecting TISHINHILITI A - 1+24 = -+ Gta rite 29t = 3tz -@ 4 -4 ti = \+2t2 -③

Salve 3 ç@ . ti = u Ź E t = 1/2 Sub in Rruation ④ 1 + 2xl - 14 Gr! 2 - av so the two lines intersects. .-=[2]+) 1 2 1 + 1 lo tresecting point li - <2,21,2> و ما ν تم d mind

b) plane contains li se la AN Nwan O- *0.1175 () 7-8) Nwa h Vector forms is and paralled to a (1,2,4) plane ebaine contain a u 1 2 1 and non un ī U XV = 1 1 2 - 4 Jo 32 =(-2-12) – j (4 – 24) +k(6-(-5)) 3.-141 +20j +12K -19 ūrūza-03) CX

plane equation. 8.5=an 7.(-03):23) _ -14+40 +48 12) - 142 +20yti2z = 74 74 -72 +10y +62 = 37