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Prove that for all values of lambda an...

Prove that for all values of `lambda` and `mu` , the planes `(2x)/a+y/b+(2z)/c-1+lambda(x/a-(2y)/b-z/c-2)=0` and `(4x)/a-(3y)/b-5+mu((5y)/b+(4z)/c+3)=0` intersect on the same line.

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CENGAGE PUBLICATION-THREE DIMENSIONAL GEOMETRY-All Questions
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  2. O A ,O Ba n dO C ,w i t hO as the origin, are three mutually perpen...

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  3. Prove that for all values of lambda and mu , the planes (2x)/a+y/b+(...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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