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Let P1,  P2 and P3 denote. respectively, the planes defined by
a1x+b1y+c1z= = α1
a2x + b2y+c2z= α2
a3x-b3y + c3z = α3
It is given that P1, P2, P3 intersect exactly at one point when α1 = α2 = α3 = 1, If now
α1 = 2, α2 = 3 and α3 = 4 then the planes
  • a)
     do not have any common point of intersection.
  • b)
     intersect at a unique point
  • c)
     intersect along a straight line
  • d)
     intersect along a plane
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
Let P1,P2and P3denote. respectively, the planes defined bya1x+b1y+c1z=...
The matrix form.Ax =  B is
If α1 = α2 = α3 = 1, then this system have a unique solution.
Hence rank (A) = rank (A  | B) = 3 (Number of variables)
If we change α 1= 2, α2 = 3, α3 = 4, still rank (A) = rank (A|B)= 3
Hence plane intersect at a unique point.
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Let P1,P2and P3denote. respectively, the planes defined bya1x+b1y+c1z= = α1a2x + b2y+c2z= α2a3x-b3y + c3z =α3It is given that P1, P2, P3intersect exactly at one point when α1= α2= α3= 1, If nowα1= 2, α2= 3 and α3= 4 then the planesa)do not have any common point of intersection.b)intersect at a unique pointc)intersect along a straight lined)intersect along a planeCorrect answer is option 'B'. Can you explain this answer?
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Let P1,P2and P3denote. respectively, the planes defined bya1x+b1y+c1z= = α1a2x + b2y+c2z= α2a3x-b3y + c3z =α3It is given that P1, P2, P3intersect exactly at one point when α1= α2= α3= 1, If nowα1= 2, α2= 3 and α3= 4 then the planesa)do not have any common point of intersection.b)intersect at a unique pointc)intersect along a straight lined)intersect along a planeCorrect answer is option 'B'. Can you explain this answer? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about Let P1,P2and P3denote. respectively, the planes defined bya1x+b1y+c1z= = α1a2x + b2y+c2z= α2a3x-b3y + c3z =α3It is given that P1, P2, P3intersect exactly at one point when α1= α2= α3= 1, If nowα1= 2, α2= 3 and α3= 4 then the planesa)do not have any common point of intersection.b)intersect at a unique pointc)intersect along a straight lined)intersect along a planeCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let P1,P2and P3denote. respectively, the planes defined bya1x+b1y+c1z= = α1a2x + b2y+c2z= α2a3x-b3y + c3z =α3It is given that P1, P2, P3intersect exactly at one point when α1= α2= α3= 1, If nowα1= 2, α2= 3 and α3= 4 then the planesa)do not have any common point of intersection.b)intersect at a unique pointc)intersect along a straight lined)intersect along a planeCorrect answer is option 'B'. Can you explain this answer?.
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