- Lit 1 hr the

x = (OT 210) + 01, 0, 2) a P.M!. 2 ViVtill:11111.LatiOILS, thi7 –

where / E

where E R.,

(fir lines that itre or to the line II and intersect it at the point 01 21(0 1[2 markil (b) If we were to find. uslid. solution to (t) by starting with ii xio = (a, b, 0, whist must be true about Vhi.H.161.1.11. u, b E., outer for it L+011.1.1U011. tai 11,Cist?j.vii rutLivining. inark41

[S ‘) 6 1.9 2. Thi-s impurritcAll matrix rupresents 3 planes (3 general eq(Uation_s) that intersect_ El 1 -3 12 1 1 -1 • g (a) Stilve the equaiticifs, howing your working_ (3 111/11:1(- Ii) In (N)., you fount’ a singlt. point P at which Owh 3 planes Efliff’Slifitef I by an augmented matrix inter_4ectecl, Find a 4th plane that MiltailL4 [HAIL eiLL’ [Mint p, dna the 4:prig”’. Maki,. is vortor enuation for your 4th plane. of the form

x – lw - This. augmented mat L1111EINfirlt,14 3 planfs_ It does wit have a unique solution_

1 1 -2 2 1 -3 6 4 -10

,(11]

0 C

(2 marks]

(a) Fill(‘ Ulf, mike t Mist gives infinite. sralistiorLs. Sketch (iv write rL gelimetriv ficscription. of how pinnils intersect_ inarkbq (I)) thing your value for (7, found it (a), (40 4 to-rorflinate where the 3 planes ineet.r mid i vector eilittrLt4111 of the W bere 41.1 3 ptitniis meet_ 4 marli.4 Find i 440111:11LLit 4t Ii plane thitt woutd interwct the (Alter 3 pilules an till! line ‘rotund it’ (b), Give the equation of p.m( plane in. General form_ ‘2 marks]

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