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The intersection of the spheres x^2+y...

The intersection of the spheres `x^2+y^2+z^2+7x-2y-z=13a n dx^2+y^2=z^2-3x+3y+4z=8` is the same as the intersection of one of the spheres and the plane a. `x-y-z=1` b. `x-2y-z=1` c. `x-y-2z=1` d. `2x-y-z=1`

A

`x-y-z=1`

B

`x-2y-z=1`

C

`x-y-2z=1`

D

`2x-y-z=1`

Text Solution

Verified by Experts

The correct Answer is:
d
The given spheres are
`x^(2)+y^(2)+7x-2y-z-13=0" "(i)`
and `x^(2)+y^(2)+z^(2)-3x+3y+2-8=0" "(ii)`
Subtracting (ii) from (i), we get
`10x-5y-5z-5=0`
or `2x-y-z=1`
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CENGAGE-THREE-DIMENSIONAL GEOMETRY -Exercise (Single)
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  2. If the angle theta between the line (x+1)/1=(y-1)/2=(z-2)/2 and the pl...

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  3. The intersection of the spheres x^2+y^2+z^2+7x-2y-z=13a n dx^2+y^2=...

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  4. If a plane cuts off intercepts OA = a, OB = b, OC = c from the coordi...

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  7. A tetrahedron has vertices O(0,0,0),A(1,2,1),B(2,1,3),a n dC(-1,1,2), ...

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  8. The radius of the circle in which the sphere x^(I2)+y^2+z^2+2z-2y-4z...

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  9. The lines (x-2)/1=(y-3)/2=(z-4)/(-k)a n d=(x-1)/k=(y-4)/2=(z-5)/1 are ...

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  10. The point of intersection of the lines (x-5)/3=(y-7)/(-1)=(z+2)/1a ...

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  11. Two system of rectangular axes have the same origin. IF a plane cuts t...

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

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  13. The dr. of normal to the plane through (1,0,0), (0,1,0) which makes an...

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  14. The centre of the circle given by vecr.(hati+2hatj+2hatk)=15and|vecr-(...

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