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A variable plane l x+m y+n z=p(w h e r e...

A variable plane `l x+m y+n z=p(w h e r el ,m ,n` are direction cosines of normal`)` intersects the coordinate axes at points`A ,Ba n dC` , respectively. Show that the foot of the normal on the plane from the origin is the orthocenter of triangle `A B C` and hence find the coordinate of the circumcentre of triangle `A B Cdot`

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CENGAGE PUBLICATION-THREE DIMENSIONAL GEOMETRY-All Questions
  1. If P is any point on the plane l x+m y+n z=pa n dQ is a point on the l...

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  2. find the equation of the plane with intercepts 2,3 and 4 on the x, y a...

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  3. A variable plane l x+m y+n z=p(w h e r el ,m ,n are direction cosines ...

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  4. If a line makes angles alpha,betaa n dgamma with three-dimensional c...

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  5. A plane which is perpendicular to two planes 2x-2y+z=0 and x-y+2z = 4 ...

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  6. Let x-ysin alpha-zsin beta=0,xsin alpha+zsin gamma-y=0 and xsin beta+y...

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  7. The position vectors of the four angular points of a tetrahedron OABC ...

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  8. Find the distance of the point (-2,3,-4) from the line ("x"+2)/3=(2"...

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  9. The plane 4x+7y+4z+81=0 is rotated through a right angle about its ...

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  10. If (a, b, c) is a point on the plane 3x + 2y + z = 7, then find the ...

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  11. Let the equation of the plane containing the line x-y - z -4=0=x+y+ 2z...

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  12. Let a1, a2, a3.......... be in A.P. and h1,h2,h3.....,in H.P. If a1=2 ...

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  13. If the angle between the plane x-3y+2z=1 and the line (x-1)/2=(y-1)/...

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  14. The length of projection of the line segment joining the points (1,...

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  15. Find the equation of a plane passing through (1, 1, 1) and parallel to...

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  16. Find the equation of the plane passing through the points(2,1,0),(5,0,...

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  17. Find the direction cosines of the line (x-1)/(1)=(y-2)/(2)=(z-3)/(3),

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  18. The value of m for which straight lein 3x-2y+z+3=0=4 x-3y+4z+1 is pa...

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  19. Let the equations of a line and plane be (x+3)/2=(y-4)/3=(z+5)/2a n...

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  20. The length of the perpendicular form the origin to the plane passin...

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