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Prove that if a plane has intercepts a,b...

Prove that if a plane has 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`.

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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

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If p is the length of perpendicular from the origin to the line whose intercepts on the axes are a and b, then show that 1/p^2=1/a^2+1/b^2 .

If p is the length of perpendicular from the origin to the line whose intercepts on the axes are a and b, then show that (1)/(p^(2)) = (1)/(a^(2)) +(1)/(b^(2)) .

If p_1, p_2, p_3 are the altitudes of a triangle from the vertices A, B, C and triangle , the area of the triangle, prove that : 1/p_1+1/p_2-1/p_3= (2ab)/((a+b+c)triangle) cos^2 frac (C)(2) .

A variable plane which is at a constant distance 6 p from the origin meets the axes in points A, B and C respectively. Show that the locus of the centroid of Delta ABC is 1/x^2+1/y^2+1/z^2=1/(4p^2)

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PRADEEP PUBLICATION-THREE DIMENSIONAL GEOMETRY-EXERCISE
  1. Find the vector equation of the line passing through (1, 2, 3) and par...

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  2. Find the equations of the straight line passing through the point (1, ...

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  3. Prove that if a plane has intercepts a,b,c and is at a distance of p u...

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  4. Distance between the two planes: 2x+3y+4z=4 and 4x+6y+8z = 12 is:

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  5. The planes 2x - y + 4z = 5 and 5x - 2.5y + 10z = 6 are :

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  6. If a line makes angle 90^(@),135^(@),45^(@) with X,Y and Z-axis respec...

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  7. The vector equation of the line through the points (3, 4, - 7) and (1,...

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  8. Fill ups Equations of a line containing the points (0,0,0) and (1,2,-3...

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  9. If cos alpha , cos beta, cos gamma are the direction-cosines of a line...

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  10. Fill ups If the lines (x-1)/2=(y+2)/-3=(z-4)/lambda and x/1=y/-2=z/2 a...

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  11. The vector equation of the line (x-5)/(3)=(y+4)/(7)=(z-6)/(2) is ........

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  12. Fill ups The direction cosines of the vector 3hati+2hatj-6hatk are…………...

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  13. Direction cosines of hat i are ‘

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  14. Fill ups The equation of the plane containing the points (2,0,0),(0,3,...

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  15. Fill ups A plane 'p' passes through the point P(1,-2,3). If O is the o...

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  16. Find the cartesian equation of the following planes. vecr.(hati+hatj-h...

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  17. If a line makes an angle of (pi)/(4) each of y and z axis, then the an...

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  18. Fill ups The equation of the plane containing the points (2,0,0),(0,3,...

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  19. Fill ups Distance of the point (4,-2,3) from Y-axis is……………… .

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  20. Fill ups Intercepts made by the plane 2x-3y+5z-30=0 on the coordinate ...

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