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A variable plane moves in such a way tha...

A variable plane moves in such a way that the sum of the reciprocals of its intercepts on the three coordinate axes is constant. Show that the plane passes through a fixed point.

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Given,
equation of Plane
` x/a​+y/b​+z/c​=1 `
Intercepts of plane
`A(a,0,0),B(0,b,0),C(0,0,c) `
`1/a​+1/b​+1/c​=1 ` ...
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RD SHARMA-THE PLANE -Solved Examples And Exercises
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  2. Find the equation of the plane through the points A(2,2,-1),B(3,4,2)a ...

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  3. A variable plane moves in such a way that the sum of the reciprocals o...

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  4. A plane meets the coordinate axes in A ,B ,C such that eh centroid of ...

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  5. Write the equation of the plane whose intercepts on the coordinate axe...

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  6. Show that the four point (0,-1,-1),(4,5,1),(3,9,4)a n d(-4,4,4) are co...

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  7. Find the image of the point (1,3,4) in the plane 2x-y+z+3=0.

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  8. Find the image of the point with position vector 3 hat i+ hat j+2 hat ...

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  9. Find the length and the foot of perpendicular from the point (1,3//...

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  10. Find the distance between the point with position vector hat i-5 hat ...

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  11. Find the equation of the plane through the intersection of the planes ...

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  12. Show that the plane whose vector equation is vec rdot( hat i+2 hat j-...

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  13. Prove that the lines (x+1)/3=(y+3)/5=(z+5)/7a n d(x-2)/1=(y-4)/4=(z-6)...

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  14. Show that the lines vec r=( hat i+ hat j- hat k)+lambda(3 hat i- hat ...

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  15. Find the distance of the point P(-1,-5,-10) from the point of intersec...

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  16. Find the distance of the point (1,-2,3) from the plane x-y+z=5 measure...

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  17. Show that the plane whose vector equation is vec r*( hat i+2 hat j= h...

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  18. Find the equation of the plane passing through the point (0,7,-7) and...

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  19. Find the equation of the plane passing through the points (1,-1,2)a n ...

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  20. Find the equation of the plane passing through the point whose coor...

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