Find the coordinates of the foot of perpendicular drawn from the pointA(−1;,8,4)to the line joining the pointsB(0,−1;,3)andC(2,−3,−1;).Hence, find the image of the pointAin the lineBC.Find the coordinates of the foot of perpendicular drawn from the pointA(−1;,8,4)to the line joining the pointsB(0,−1;,3)andC(2,−3,−1;).Hence, find the image of the pointAin the lineBC.A(−1;,8,4)A(−1;,8,4)A(−1;,8,4)AA((−−1;1,,88,,44))B(0,−1;,3)B(0,−1;,3)B(0,−1;,3)BB((00,,−−1;1,,33))C(2,−3,−1;).C(2,−3,−1;).C(2,−3,−1;).CC((22,,−−33,,−−1;1))..AAAAABC.BC.BC.BBCC..?<p></p>

Find the coordinates of the foot of perpendicular drawn from the pointA(−1;,8,4)to the line joining the pointsB(0,−1;,3)andC(2,−3,−1;).Hence, find the image of the pointAin the lineBC.Find the coordinates of the foot of perpendicular drawn from the pointA(−1;,8,4)to the line joining the pointsB(0,−1;,3)andC(2,−3,−1;).Hence, find the image of the pointAin the lineBC.A(−1;,8,4)A(−1;,8,4)A(−1;,8,4)AA((−−1;1,,88,,44))B(0,−1;,3)B(0,−1;,3)B(0,−1;,3)BB((00,,−−1;1,,33))C(2,−3,−1;).C(2,−3,−1;).C(2,−3,−1;).CC((22,,−−33,,−−1;1))..AAAAABC.BC.BC.BBCC..?

Solution:

The direction ratios of line joining pointsBandCare2,−2;,−4The equation of line joining pointsBandCisx−02=y+1−2;=z−3−4Let the foot of perpendicular from pointA(−1;,8,4)on lineBCbeD(x,y,z),x=2k,y=−1;−2;k,z=3−4k, wherekis real number.The direction ratios of line perpendicular toBCis2k+1,−9−2;k,−1;−4kTherefore we have(2k+1)(2)+(−9−2;k)(−2;)+(−1;−4k)(−4)=0, which gives24k+24=0, which impliesk=−1;So the pointDis(−2;,1,7)The image of pointAin the lineBCbeE(p,q,r)We have−2;=(p−1;)2,1=(q+8)2,7=(r+4)2So we getp=−3,q=−6;,r=10.So the pointEis(−3,−6;,10).

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