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Q:- Two systems of rectangular axes have the same origin. If a plane cuts them at distances a,b,c and a 1 ,b 1 ,c 1 from the origin, then A.(1/a^2)+(1/b^2)+(1/c^2)=(1/a 1 ^2)+(1/b 1 ^2)+(1/c 1 ^2) B. (1/a^2)-(1/b^2)+(1/c^2)=(1/a 1 ^2)-(1/b 1 ^2)+(1/c 1 ^2) C. (a^2)+(b^2)+(c^2)=(a 1 ^2)+(b 1 ^2)+(c 1 ^2) D.(a^2)-(b^2)+(c^2)=(a 1 ^2)-(b 1 ^2)+(c 1 ^2)

Q:- Two systems of rectangular axes have the same origin. If a plane cuts them at distances a,b,c and a1,b1,c1 from the origin, then


A.(1/a^2)+(1/b^2)+(1/c^2)=(1/a1^2)+(1/b1^2)+(1/c1^2)


B. (1/a^2)-(1/b^2)+(1/c^2)=(1/a1^2)-(1/b1^2)+(1/c1^2)


C. (a^2)+(b^2)+(c^2)=(a1^2)+(b1^2)+(c1^2)


D.(a^2)-(b^2)+(c^2)=(a1^2)-(b1^2)+(c1^2)

Grade:12

1 Answers

Badiuddin askIITians.ismu Expert
147 Points
11 years ago

Dear Tapasranjan

equation of planes are 

x/a + y/b + z/c =1

and

 x/a1  + y/b1 + z/c1 =1

since the axis is roatated but the origin and the plane is same so perpendicular distance from the origine to both the plave will be same

|1|/√{1/a2 + 1/b2 +1/c2}  = |1|/√{1/a12 + 1/b12 +1/c12}

or

 √{1/a2 + 1/b2 +1/c2}  = √{1/a12 + 1/b12 +1/c12}


or

1/a2 + 1/b2 +1/c2  = 1/a12 + 1/b12 +1/c12


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Badiuddin


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