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Consider the following linear equations:...

Consider the following linear equations: `a x+b y+c z=0` `b x+c y+a z=0` `c x+a y+b z=0` Match the expression/statements in column I with expression/statements in Column II. Column I, Column II `a+b+c!=0`and `a^2+b^2+c^2=a b+b c+c a` , p. the equations represent planes meeting only at a single point `a+b+c=0a n da^2+b^2+c^2!=a b+b c+c a` , q. the equations represent the line `x=y=z` `a+b+c!=0a n da^2+b^2+c^2!=a b+b c+c a` , r. the equations represent identical planes `a+b+c!=0` and `a^2+b^2+c^2!=a b+b c+c a` , s. the equations represent the whole of the three dimensional space

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CENGAGE PUBLICATION-THREE DIMENSIONAL GEOMETRY-All Questions
  1. Consider the lines L1:(x-1)/2=y/(-1)=(z+3)/1,L2:(x-4)/1=(y+3)/1=(z+3)/...

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  2. Statement 1: A plane passes through the point A(2,1,-3)dot If distan...

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  3. Consider the following linear equations: a x+b y+c z=0 b x+c y+a z=0 c...

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  4. If the distance between the plane Ax-2y+z=d. and the plane containing ...

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  5. Prove that the volume of tetrahedron bounded by the planes vec rdo...

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  6. If a variable plane forms a tetrahedron of constant volume 64k^3 with ...

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  7. O A ,O Ba n dO C ,w i t hO as the origin, are three mutually perpen...

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

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

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

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

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

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

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

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

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

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

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

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

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