InterviewSolution
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InterviewSolution
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Find the equation of the plane through the points (2,2,1) and (9,3,6)` and perpendicular to the plane `2x+6y+6z=1`A. `x+2y-3z+5=0`B. `2x-5y+4z-8=0`C. `4x+5y-6z+3=0`D. `3x+4y-5z-9=0` |
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Answer» Correct Answer - d The equation of a plane passing through the point A(2,2,1) is `a(x-2)+b(y-2)+c(z-1)0`…………………(i) Since it passes through the point B(9,3,6), we have `a(9-2)+b(3-2)+c(6-1)=0 rArr 7a+b+5c=0`………(ii) Also, it being perpendicular to the plane `2x+6y+6z=1`, we have `2a+6b+6c=0 rArr a+3b+3c=0`. ...............(iii) On solving (ii) and (iii) by cross multiplication, we have `a/(3-15)=b/(5-21)=c/(21-1) rArr a/-12=b/-16=c/20 rArr a/3=b/4=c/-5=k` `rArr a=3k,b=4k` and `c=-5k`. substituting these values in (i), we get `3k(x-2)+4k(y-2)-5k(z-1)=0` `rArr 3(x-2)+4(y-2)-5(z-1)=0 rArr 3x+4y-5z-9=0`. |
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