Question

Find the three angles of the triangle with the given vertices: P(1,1,1), Q(1,−5,2), and R(−2,2,6)

Find a nonzero vector orthogonal to the plane through the points: A=(0,1,−1), B=(0,6,−5), C=(4,−3,−4)

Answer 1

dores of : PQ, QR and RP ame (1-1, -561,2-1) ice; (0, -6,1), .(-21, 2+5, 6-2) i. l; (-3,7,4), (1+2, 1-2, 1-6) 1.8; (3,-1,-5) respectively si sgp Recor 7 10.3–616-1) 4.(-5) Vortcort. 346-0465V p: Clos miem, ) and (le, mis tz) bei . the doors of two st. lines, then angle between them in - Cop- / lehet me thin itmilni Vhmxtos) (req.) <D&R= Cort 10-6-3)–6.7+ly Vore-65th 63747747 38 Cot?l cost 537574 CORP - copt 1-3(3)+7(-1) +4 (-5) V6-35+27514 377157f-55

los 36 (rea) 943 th of the plant A and part doros of AB are (0-0, 6-1-5+1) indy (o,s,-4) and doros of Be are (4-0,–3-6-4+5) 1 loe, (4,-9,1) . het (min) be dord of normal to the plane ABC. Hence normal in t to sr o on 2. tenee, one +5m-unto R 42 -am th =0. By cross, multiplication, 5-36 I 16 - 2 m. ory 31 = 720, +31 + 16 710, doros of normal to the plame ABC are (31,16,20). Hence a non-zero veet orthogonal to the plane ABC in oli +16) toroid)) or

where Aj i are unit vectors along noakin, Yoanis and zranis respectively,