Question

can anyone check my answers? thx!

1. In all parts of Problem 1 (this page and next), let RQ R denote the points: (a) (4 points) Find the vectors PQ from P to Q and PR from P to R. Pa= [ ] PR - [ ] (b) (4 points) Find a parametrization of the line passing through P and Q. P = Porto Wt)= 1-1 yet): - 1+3 21+) = 2+t =<1-,-1+31, 2+t> (0) (4 points) Is R on the line through P and Q? How can you tell? If R is on the line through P and PQ = t PR which means but o. t= 0 and can't be -1, so PQtt PR, SO R is not (d) (4 points) Find the orthogonal projection of PR along po. the line through Pand Projna PR = P Popa - Teat. Pū = <-1, 3, 17. 20,-2,-67 (-1,3,1) = 0-6 b. (-1,3,17 N-0² + 3² + 1² = 1 1 1 1 <-1, 3, 1>

Answer 1

solution & given Three poout Paillante ( R 13 vector form. P = î j tak 2 = oi toj +3k R = 1 -31-46 @ PR = Passition vector & -position vector e - (0.1 +zủ +31) -( 1-j tzk) = -1 + 3ỉ tk 1 Ary PR = Position vector of Ř - Position vector ? = (1-3j- 4k)-(i- ] t26) PR = 0.1 2j-sk = 21 ay Aline parallel to the vector v Ca, b, c) Passing Through the point (34,47,21) ugiven by the Parametric Equation ni xitat Y = Ytbt 2= ztet How want to find paramesic Through Palt and actul equation passing 13 FR01-0)-018] 8:14 115 shen -l-t x= It Hot y = -1+3t 2=2+t

rel we know that three point are collinear then PatPratch -11 to=-1 (not posible) since P, Q, R are not collin ear. Therefore R is not on the line through Penda. & PR = 0.7 – 2j-se and PQ = –1 +3] tk ale know that orthogonal projection of ū along b Projna = ū.I 1612 Proj PR - PR. PR se ||PRIZ Il Fall (1927 9+1)=(r =1 [{IPR 11² = 4 ] 8. R. PB = (-1 + 3) + ). (i- % -62) 20-6-6 = -12 TPR. PR = -12/ alow from Program 2 (-i+33 +) - (+3.0 ① PR = –1 +3j tk and PR = 0.1 – 25-6k PR XPR = 1 i 5 il - 31-i (18+)-j (-0) +(2-0) 1 =167-6j tak IPR XPR = -161-6j t2i = (-16, -6, 2) lo -2 -6 Any

we know that area of triangle A - 1 11 w x w l/ of a triangle formed by us and win 1 -1 +3jtK DR XPR 2-12 1-6j+2k PR = (3/= 0.1-25-66 RRX PRI = JE 16) 7+)? 4 22 a $256 +36 +4 =1296 now Areaf triangle = // - 1 1296 = 2114 - 179 Area of triangle = 574 Squase unit