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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 a1,b1,c1 from the origin, thenA.(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)

## 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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