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Question Number 46095 by Meritguide1234 last updated on 21/Oct/18

Answered by tanmay.chaudhury50@gmail.com last updated on 23/Oct/18

$$Theeqnofstlineis$$$$\frac{x-2}{1}=\frac{y-1}{2}=\frac{z-2}{3}=k$$$$eqnplanex+y+z=8$$$$(2,1,2)isapointonstline$$$$(k+2,2k+1,3k+2)isthepointwherestline$$$$intersectplane.$$$$sok+2+2k+1+3k+2=8$$$$6k+5=8k=\frac{1}{2}$$$$(\frac{5}{2},2,\frac{7}{2})isthepointwherestlineintersectplane$$$$nowwearegoingtofindimageof(2,1,2)wrtplane$$$$eqnstlinepassingthrough(2,1,2)andparallel$$$$tothenormalontheplaneis$$$$\frac{x-2}{1}=\frac{y-1}{1}=\frac{z-2}{1}=\alpha$$$$(\alpha +2,\alpha +1,\alpha +2)liesonplane$$$$\alpha +2+\alpha +1+\alpha +2=83\alpha =3\alpha =1$$$$(3,2,3)$$$$(2,1,2)(3,2,3)(a,b,c)$$$$here[(3,2,3)isfootofperpendicularand$$$$(a,b,c)isimageof(2,1,2)$$$$(3,2,3)ismidpointof(2,1,2)and(a,b,c)$$$$so\frac{2+a}{2}=3\frac{1+b}{2}=2\frac{2+c}{2}=3$$$$a=4b=3c=4$$$$\mathit{S}OTheeqnofimageofstlineisthestline$$$$passingthrough(\frac{5}{2},2,\frac{7}{2})and(4,3,4)$$$$\frac{x-\frac{5}{2}}{4-\frac{5}{2}}=\frac{y-2}{3-2}=\frac{z-\frac{7}{2}}{4-\frac{7}{2}}$$$$\frac{x-2.5}{1.5}=\frac{y-2}{1}=\frac{z-3.5}{0.5}$$$$or\frac{x-4}{1.5}=\frac{y-3}{1}=\frac{z-4}{0.5}\leftarrow imageline$$$$\mathit{P}ROJECTIONlinepassingthrough$$$$(\frac{5}{2},\frac{2}{1},\frac{7}{2})andfootofperpendicular(3,2,3)$$$$\frac{x-3}{3-2.5}=\frac{y-2}{2-2}=\frac{z-3}{3-3.5}$$$$\frac{x-3}{0.5}=\frac{y-2}{0}=\frac{z-3}{-0.5}\leftarrow plscheck...$$$$$$$$$$

Commented by tanmay.chaudhury50@gmail.com last updated on 23/Oct/18

$$thankyousirformoralboost...$$

Commented by tanmay.chaudhury50@gmail.com last updated on 23/Oct/18

Commented by Meritguide1234 last updated on 23/Oct/18

$$splendidwork$$$$$$

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