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The shortest distance from the plane 12 ...

The shortest distance from the plane `12 x+y+3z=327`to the sphere `x^2+y^2+z^2+4x-2y-6z=155` is

A

39

B

26

C

`41(4)/(13)`

D

13

Text Solution

Verified by Experts

The correct Answer is:
d
The given sphere is
`x^(2)+y^(2)+z^(2)+4x-2y-6z-155=0`
Its center is (-2,1,3) and radius `=sqrt(4+1+9+155)=sqrt169=13`

Therefore, distance of centre (-2,1,3) from the plane `12x+4y+3z=327` is
`|(12(-2)+4(1)+3(3)-327)|/(sqrt(144+16+9))`
Hence, the shortest distance is 13.
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CENGAGE-THREE-DIMENSIONAL GEOMETRY -Exercise (Single)
  1. If a plane cuts off intercepts OA = a, OB = b, OC = c from the coordi...

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  2. A line makes an angel theta with each of the x-and z-axes. If the a...

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  3. The shortest distance from the plane 12 x+y+3z=327to the sphere x^2+y^...

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

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

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

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

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

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

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  12. The lines which intersect the skew lines y=m x ,z=c ; y=-m x ,z=-c ...

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

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  14. From the point P(a ,b ,c), let perpendicualars P La n dP M be drawn to...

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  15. The plane vecr cdot vecn = q will cotain the line vecr = veca + lambda...

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  16. The projection of point P(vecp) on the plane vecr.vecn=q is (vecs), th...

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  17. The angle between hati and line of the intersection of the plane vecr...

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  18. The line (x+6)/5=(y+10)/3=(z+14)/8 is the hypotenuse of an isosceles ...

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  19. The equation of the plane which passes through the line of intersec...

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  20. Consider triangle A O B in the x-y plane, where A-=(1,0,0),B-=(0,2,0)a...

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