Question

7. Three planes can intersect in a number of different ways. For each of the combinations below, find the single point of intersection if there is one. If there isn't, explain how the planes do intersect. 71: 67 + 2+ 3z – 9 = 0 a. 12: -2x - 5y + 32 - 4 = 0 7T3 : 5x – y + 2z + 3 0 2x – 3y + 5z – 2 = 0 b. 72: -5.0 + 2y + 2z +5 = 0 -3 – 4y + 12z+1 = 0 71 : 7T3 :

Answer 1

TT, & Iu- 3y + 52-2-0 Tg 15u tay ta 245=0 ! -x + 4y +22+1 5 - 4 12 + a le a = SolM! - 25-3y +52-220 AM = (2-3 5' s! - 50+ 2y +92 +550 € 4 aut hy + 192+1200 - 4 ।२ 8(M)=P(M)=3 il cach blane intersect at point from 0 4 from ② f 8 - Dim you-54+252 lopo -54+2y+22+5fo -you- fou tuy+ y2 +1000 -5/+20y +60 24520 9+ $9200 -189-58220 butzat ay +292=0 y = 294 y=-292 a = 2-52+3y put 2=ty=-29+ H= 4y + 192+1 H=2-55+3(294) 741-39++ 12+ +) e=g-St+87t 외드시 -29 ++ lo8tt H1108.7+9) 2+897 a (9+79+) se=1tust ie (264,2) (24, 2= (1+uit,Q9,+) from 0 4 2p - 3y +52-260 -Jr + 8y + 942 +/2 20 5y + 292=0 but zat - 292, ya-29t se= 4y + 122+1 se= 41-21 t) + latt H-116 het +687 +1 sa -116tt Gott5 - 56€ ce (91962) = (5544 -992, ). ( (a+7a4), -944, 4) 5

- inlos WY 9. Costa S --5 3-4 a: 3 W Dc = 120€ Pim') bla fro 64+2y+32-9=0.0m=16 2 3 23:-9 -24-54+32-4 = 0 -2 -5 3 5r-y+22+3=0 Slm) Pim')=3 (:1m) = 1m'lo) ie each plane intersect at a point. Now, we have to find the point of intersection from to from @ f but 2y +32-9=0 -201-54+32-420 t5y + 32-4 = 0 254 +84 +102 +15=0 -274 - 72-1950 72+274 =-19 8u+7y=5 22-19-274 n = 5-74 put u=t + 8x + 7y - 520 L 8 2=-19-978 put y=tly H= 5-7Xt L 5 o 3(gat 2= 9-60-gy 87t et 2= 1 + 2 = - b et ult, a y - 14-32 +93) x = 5-7 y=-[4-3 (19-27+) +34] 319-614+) --(4) y--(4+54 +81++$+] y = - (08452181E+140] y (85+95+) 2 + [7 - 15 + 27 3 1 1 (0,19,2)= (1 +1 -11857957, 1-11-art) 2- 5 (262-105 tout-80) 21 1574121] 5-7 ta ng 157+134) 1 Now from ean 4 Gu ta 4+ 32-9=0 lon-py +42 +6=0 164 + 122-3=0 l6r+122=3 totus +32) = 3 4 1 folk but zat 4-1830-32 ( a 3 y = 4(9-32-620) x = 9-3t प te (1,14 79=(1-3%, sang (1-31-60% - 2+1] 37 - 37 + 1 t 12-247-27+36+ & (rreth y + ( 45+12+) 16