InterviewSolution
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InterviewSolution
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Find ten equation of the plane passing through the point `(0,7,-7)`and containing the line `(x+1)/(-3)=(y-3)/2=(z+2)/1`. |
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Answer» The general equation of the plane passing through the point (0,7,-7) is given by `a(x-0)+b(y-7)=0 If (i) contains the given line then it must pass through the point *-1,3,-2) and must be parallel to the given line If (i) passes through the point (-1,3,-2) we have a(-1-0)+b(3-7)+c(-2+7)=0 rarr a+4b-5c=0 If (i) is parallel to the given line then its normal should be perpendicular to htis line `therefore (-3) a+2b+1xxc=0 rarr -3a+2b+c=0` on solving (ii) and (iii) by cross multiplication we get `rarr (A)/(1)=(b)/(1)=(c )/(1) = lambda`(say) Then `a=lambda, b = lambda` and `c = lambda` Putting `a=lambda , b = lambda` and `c = lambda` in we get `lambda x+lambda(y-7) + lambda(z+7) =0 rarr x + (y-7) + (z+7)=0` `rarr x+y+z=0` Hence the required equation of the plane is x + y Z=0 |
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