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Show that the plane 2x-2y+z+12=0 touches...

Show that the plane `2x-2y+z+12=0` touches the sphere `x^2+y^2+z^2-2x-4y+2z-3=0.`

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The shortest distance from the plane 12 x+4y+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

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CENGAGE PUBLICATION-THREE DIMENSIONAL GEOMETRY-All Questions
  1. A sphere of constant radius k passes through the origin and meets the ...

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  2. A variable plane passes through a fixed point (a ,b ,c) and cuts the...

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  3. Show that the plane 2x-2y+z+12=0 touches the sphere x^2+y^2+z^2-2x-4y+...

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  4. If O is the origin, OP = 3, with direction ratios -1, 2 and -2, then f...

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  5. If P(x,y,z) is a point on the line segment joining Q(2,2,4) and R(3,5,...

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  6. If vecr is a vector of magnitude 21 and has direction ratios 2, -3 an...

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  7. Find the distance of the point P(a ,b ,c) from the x-axis.

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  8. A line makes angles alpha,betaa n dgamma with the coordinate axes. If ...

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

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  10. Find the distance between the parallel planes x+2y-2z+1=0a n d2x+4y...

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  11. A ray of light passing through the point A(1,2,3) , strikews the pl...

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  12. The plane a x+b y=0 is rotated through an angle alpha about its line...

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  13. Find the equation of a plane containing the line of intersection of...

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  14. Find the locus of a point, the sum of squares of whose distance from t...

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  15. Find the length and the foot of the perpendicular from the point (7...

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  16. Find the angle between the lines vec r= dot( hat i+2 hat j- hat k)+la...

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  17. Find the equation of the projection of the line (x-1)/(2)=(y+1)/(-1)=(...

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  18. Find the equation the plane which contain the line of intersection ...

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  19. Find the vector equation of the line passing through (1,2,3) and par...

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  20. Find the distance of the point P(3,8,2) from the line 1/2(x-1)=1/4(...

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