Question

please answer question 16 and 17

17. Find the equation of a plane that passes through the points (15,5, 2), (6, 2, 1) and (10,3, 2). Does the point (-2,-5, -3) lie on the plane? [5 marks)

Answer 1

04 BOAS PAGE NO :04 DATE: 17. Solutions Equation of plane plane passing through points A 115, 5,2) B16,2,1) c(1032) vector equation of a plane paceing through three position vectors is points with (-a). [15-a)x(2-a)] Now the plane passes through the points B 16,2,1) c (10,32) A 115,5,2) ? - 108 + 32 +22 Befort to bît 27+ 12 å = 15 ît 5j + 221 Now, (bê+ 2a + 1 ů) - lisi+ S9+ 28) to -g ? -3 9 - 1 (10 8 + 3 + 2F) (15 i +59 + 2 E) 1 le-a) -5 î -2 9 to 16-a) x (2-a) A -3 2.

PAGE NO: 02 DATE: ilo-2) - j (0-5) + jê 118-15) -2 + 5 + 3 Vector O equation of plage (from 1 8- (152 +59 +2 R) -2; + 5j +316) - finding carstenian equation, Deut gnityj+z12 Ini + gå + 2,2) - (15ê + 5j +2 % +53 +9 ) - | -22 +53 +1312) (x - 5) + (-5) + (2-2) (-24+55+ 3 ) -2 (1-15) 514-5) + 3 ( 2-2) CI ST + - 2n + 30 Sy 25 + 32-6 -2n+ sy + 32-1 lie on a lere gf point the plone then it will satisfy the equation of plane. So Check for (-2,-5-3) -21-2) + 51-5)+31-3) 4 - 25 -9 - 1 - 31 & o So this point lie the plone do not

PAGE NO: 03 DATE: 16 passing through (a,b,c) and Equatron al line having direction copines (e,m,,n) is given as y-b 2-c n-a li Here line passes through point Equation of line. N-2 y+3 2-1 l Now line 0 perpendicular to the given line. M71 2+2 5 3 line 6 I line 2 112,-3,1) So dot product of P both direction cosiny must be Zero, + m, jt n (2) (3 + 27 +56) 31, + 25m + 5n, 3. We do not have any other condition values. given by which find l, m, n, we can

PAGE NO: ou DATE: So line are unable to Ana direction cosines of Equation of line form in symmetric 7-2 m2 4+3 2-1 ma ni where equation 3l + 2m + 50, no. l=1 m = 1 n = -1 satisfy 32, + 2m + 5n = 0 as 31+ 20-5(1)=0. So the equation will become eatiefres the for enample: this will 2-1 Y+3 1 1 -1 f Symmetric form > Equation of line in parametric form 7.1 t: 1-2 y +3 mo n=t(e, 72 m. lt)-3 = n. 1t) + 1 af put we m,-1, 3, 2-1 then, ++2 z = n = 4 1-3 -t+1 7 Parametric form Ansman