InterviewSolution
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InterviewSolution
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(i) Find the equation ofthe plane passing through the points`(2,1,0),(5,0,1)a n d(4,11)dot`(ii) If `P`s the point `(2,1,6),`then the find the point `Q`such that `P Q`is perpendicular to the plane in (i) and themidpoint of `P Q`lies on it. |
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Answer» Correct Answer - (i) `x+y-2z=3" "(ii) Q(6,5,-2)` (i) Equation of plane passing throuth (2,1,0) is `a(x-2)+b(y-1)+c(z-0)=0` It also passes through (5,0,1) and (4,1,1). `implies3a-b+c=0" and "2a-0b+c=0` On solving, we get `(a)/(-1)=(b)/(-1)=( c )/(2)` `:.` Equation of plane is `-(x-2)-(y-1)+2(z-0)=0` `-(x-2)-y+1+2z=0` `implies" "x+y-2z=3` (ii) Let the coordinates of Q be `(alpha,beta,gamma).` Equation of line `PQimplies(x-2)/(1)=(y-1)/(1)=(z-6)/(-2)` Since, mid-point of P and Q `((alpha+2)/(2),(beta+1)/(2),(gamma+6)/(-2)),` which lies in line PQ. `implies" "((a-2)/(2)-2)/(2)=((beta+1)/(2)-1)/(1)=((gamma+6)/(2)-6)/(-2)` `(1((alpha+2)/(2)-2)+1((beta+1)/(2)-1)-2((gamma+6)/(2)-6))/(1.1+1.1+(-2)(-2))=2` `[because((alpha+2)/(2))-1((beta+1)/(2))-2((gamma+6)/(2))=3]` `impliesalpha=6,beta=5,gamma=-2impliesQ(6,5,-2)` |
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