InterviewSolution
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InterviewSolution
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Find the vector equation of the plane passing thrugh the points (2,5,-3),(-2,-3,5),(5,3,-3). |
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Answer» The equation of the plane passing through the point A(2,5,-3) is given by `a(x-2)+b(y-5)+c(z+3)=0`. If the plane passes through the points B(-2,,-3,5) and C(5,3,-3), then we have `a(-2-2)+b(-3-5)+c(5+3)=0 rArr -4a-8b+8c=0`……………(i) If the plane passes through the points B(-2,-3,5) and C(5,3,-3), then we have `a(-2-2)+b(-3-3)+c(5+3)=0 rArr -4a-8b+8c=0.............(ii)` `a(5-2)+b(3-5)+b(3-5)+c(-3+3)=0 rArr 3a-2b+0c=0`..................(iii) On solving (ii) and (iii) by cross multiplication, we get `a/(0+16)=b/(24-0)=c/(8+24) rArr a/16=b/24=c/32` `rArr a/2=b/3=c/4=k` (say) `rArr a=2k, b=3k` and `c=4k`. Putting these values of a,b and c in (i), we get `2k(x-2)+3k(y-5)+4k(z+3)=0` `rArr 2(x-2)+3(y-5)+4(z+3)=0` `rArr 2(x-2)+3(y-5)+4(z+3)=0` `rArr 2x+3y+4z-7=0`. Hence, the required equation of the plane is `2x+3y+4z-7=0`. |
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