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The points A(2-x,2,2), B(2,2-y,2), C(2,2...

The points `A(2-x,2,2), B(2,2-y,2), C(2,2,2-z)` and `D(1,1,1)` are coplanar, then locus of `P(x,y,z)` is

A

`1/x+1/y+1/z=1`

B

`x+y+z=1`

C

`1/(1-x)+1/(1-y)+1/(1-z)=1`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
We have
`vec(AB)=xhati-yhatj,vec(AC)=xhati-zhatk,vec(AD)=(x-1)hati-hatj-hatk`
Clearly these vectors are coplanar.
`:.|(x,-y,0),(x,0,-z),(x-1,-1,-1)|=0implies1/x+1/y+1/z=1`
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OBJECTIVE RD SHARMA ENGLISH-PLANE AND STRAIGHT LINE IN SPACE -Section I - Solved Mcqs
  1. Let the pairs veca, vecb and vecc vecd each determine a plane. Then th...

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  2. The equation of the plane containing the lines vecr = vec a (1) + lam...

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  3. The points A(2-x,2,2), B(2,2-y,2), C(2,2,2-z) and D(1,1,1) are coplana...

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  4. Find the vector equation of the plane in which the lines vecr=hati+ha...

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  5. The equation of the plane which contains the origin and the line of in...

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  6. The length of the perpendicular from the origin to the plane passing t...

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

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  8. The equation of the plane which bisects the line joining (2, 3, 4) and...

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  9. Distance of the point P(vecp) from the line vecr=veca+lamdavecb is ...

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  10. Distance of the point P(x2, y2, z2) from the line (x-x1)/l=(y-y1)/m=(z...

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  11. If veca,vecb and vecc are three non-coplanar vectors then the length o...

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  12. If P(0, 1, 0) and Q(0, 0 1) are two points, then the projection of PQ ...

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  13. A plane passes through the point (1, 1, 1). If b, c, a are the direc...

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  14. If the foot of the perpendicular from O(0,0,0) to a plane is P(1,2,2)....

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  15. The equation of the plane through the point (1,2,3) and parallel to th...

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  16. The straight line (x-3)/3=(y-2)/1=(z-1)/0 is Parallel to x-axis Parall...

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  17. The direction ratios o f a normal to the plane through (1,0,0) and (0,...

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  18. Find the equation of a plane which passes through the point (3, 2, 0...

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  19. If the lines (x-1)/2=(y+1)/3=(z-1)/4a n d(x-3)/1=(y-k)/2=z/1 intersect...

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  20. The lines (x-2)/(1) = (y-3)/(1) =(z-4)/(-k) and (x-3)/(k)=(y-4)/(1) = ...

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