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A variable plane moves so that the sum o...

A variable plane moves so that the sum of the reciprocals of its intercepts on the coordinate axes is `(1//2)`. Then, the plane passes through the point

A

`(0,0,0)`

B

(1,1,1)

C

`(1/2,1/2,1/2)`

D

`(2,2,2)`

Text Solution

Verified by Experts

The correct Answer is:
d
Let the required equation of the plane be `x/a+y/b+z/c=1`.
Then, `1/a+1/b+1/c =1/2 rArr 2/a+2/b+2/c=1`.
It means that the plane passes through the point (2,2,2).
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RS AGGARWAL-THE PLANE-Objective Questions
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  2. The angle between the line (x+1)/1=y/2=(z-1)/1 and a normal to the pla...

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  3. The point of intersection of the line (x-1)/3=(y+2)/4=(z-3)/-2 and the...

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  4. The equation of a plane passing throgh the points A(a,0,0), B(0,b,0) a...

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  5. If theta is the angle between the planes 2x-y+2z=3 and 6x-2y+3z=5, the...

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  6. The angle between the planes 2x-y+z=6 and x+y+2z=7, is

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  7. The angles between the planes vecr.(3hati-6hatj+2hatk)=4 and vecr.(2ha...

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  8. The equation of a plane through the point (2, 3, 1) and (4, -5, 3) and...

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  9. A variable plane moves so that the sum of the reciprocals of its inter...

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  10. The equation of a plane which is perpendicular to (2hati-3hatj+hatk) a...

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  11. The equation of the plane passing through the point A(2,3,4) and paral...

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  12. The foot of the perpendicular from the point A(7,14,5) to the plane 2x...

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  13. The equation of the plane which makes with coordinate axes, a triangle...

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  14. The intercepts made by the plane vecr.(2hati-3hatj+4hatk)=12 are

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  15. The angle between the line (x-2)/1=(y+3)/-2=(z+4)/-3 and the plane 2x-...

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  16. The angle between the line vecr=(hati+hatj-3hatk)+lambda(2hati+2hatj+h...

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  17. Find the distance of the point (1,2,5) from the plane vecr.(hati+hatj+...

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  18. The distance between the parallel planes 2x-3y+6z=5 and 6x-9y+18z+20=0...

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  19. The distance between the planes x+2y-2z+1=0 and 2x+4y-4z+5=0, is

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  20. The image of the point (1, 3, 4) in the plane 2x-y+z+3=0 is (3,\ 5,\ 2...

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