Home
Class 12
MATHS
Prove that if a plane has the intercept...

Prove that if a plane has the intercepts a, b, c and is at a distance of p units from the origin, then `1/(a^2)+1/(b^2)+1/(c^2)=1/(p^2)`.

Promotional Banner

Topper's Solved these Questions

  • THREE DIMENSIONAL GEOMETRY

    MODERN PUBLICATION|Exercise COMPETITION FILE|25 Videos

  • RELATIONS AND FUNCTIONS

    MODERN PUBLICATION|Exercise CHAPTER TEST (1)|12 Videos

  • VECTOR ALGEBRA

    MODERN PUBLICATION|Exercise CHAPTER TEST 10|12 Videos

Similar Questions

Explore conceptually related problems

If a plane has intercepts a,b,c on axes and is at a distance of p units from the origin then prove that 1/a^2+1/b^2+1/c^2=1/p^2

Two systems of rectangular axes have the same origin. If a plane cuts them at distance a ,b ,cand a^prime ,b^(prime),c ' from the origin, then a. 1/(a^2)+1/(b^2)+1/(c^2)+1/(a^('2))+1/(b^('2))+1/(c^('2))=0 b. 1/(a^2)-1/(b^2)-1/(c^2)+1/(a^('2))-1/(b^('2))-1/(c^('2))=0 c. 1/(a^2)+1/(b^2)+1/(c^2)-1/(a^('2))-1/(b^('2))-1/(c^('2))=0 d. 1/(a^2)+1/(b^2)+1/(c^2)+1/(a^('2))+1/(b^('2))+1/(c^('2))=0

If "P" is the distance from the origin to (x)/(a)+(y)/(b)=1 then (1)/(a^(2))+(1)/(b^(2))

Two system of rectangular axes have the same origin. IF a plane cuts them at distances a,b,c and a\',b\',c\' from the origin then (A) 1/a^2+1/b^2-1/c^2+1/a^(\'2)+1/b\^(\'2)-1/c^(\'2)=0 (B) 1/a^2-1/b^2-1/c^2+1/a^(\'2)-1/b\^(\'2)-1/c^(\'2)=0 (C) 1/a^2+1/b^2+1/c^2-1/a^(\'2)-1/b\^(\'2)-1/c^(\'2)=0 (D) 1/a^2+1/b^2\+1/c^2+1/a^(\'2)+1/b\^(\'2)+1/c^(\'2)=0

A plane makes intercepts 1,2, 3 on the coordinate axes. If the distance from the origin is p, then the value of p is

Find the vector equation of the plane passing through the points A(a,0,0),B(0,b,0) and C(0,0,c) . Reduce it to normal form.If plane ABC is at a distance p from the origin,prove that (1)/(p^(2))=(1)/(a^(2))+(1)/(b^(2))+(1)/(c^(2))

The line L has intercepts a and b on the coordinate axes. The coordinate axes are rotated through a fixed angle, keeping the origin fixed. If p and q are the intercepts of the line L on the new axes, then (1)/(a^(2))-(1)/(p^(2))+(1)/(b^(2))-(1)/(q^(2)) is equal to

If p_(1),p_(2),p_(3) are altitude of a triangle ABC from the vertices A,B,C and Delta the area of the triangle, then (1)/(p_(1)^(2))+(1)/(p_(2)^(2))+(1)/(p_(3)^(2))=

Two systems of rectangular axes have the same origin. If a plane cuts them at distances a ,b ,ca n da^(prime),b^(prime),c^(prime) respectively, prove that 1/(a^2)+1/(b^2)+1/(c^2)=1/(a^('2))+1/(b^('2))+1/(c^('2))