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Show that the plane 2x-y-2z-4=0 touches ...

Show that the plane `2x-y-2z-4=0` touches the shpere `x^2+y^2+z^2+2x-6y+1=0`.

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Equation of the sphere concentric to the given sphere and passing through origin is `x^2+y^2+z^2-4x-6y+8z=0`.
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MBD PUBLICATION-THREE DIMENSIONAL GEOMETRY-QUESTION BANK
  1. Find the equation of the line through (-1,0,1) and perpendicular to th...

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  2. Show that the lines (x+3)/2=(y+5)/3=(z-7)/-3and (x+1)/4=(y+1)/5=(z+1)/...

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  3. Show that the plane 2x-y-2z-4=0 touches the shpere x^2+y^2+z^2+2x-6y+1...

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  4. Find the equation of the sphere concentric with the sphere x^2+y^2+z^2...

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  5. Find equation of the sphere whose centre is (2,-3,4) and which passes ...

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  6. Find equation of the sphere with centre (3,6,-4) and touching the plan...

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  7. Find equation of the sphere passing through the points (0,0,0), (2,0,0...

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  8. If one end of a diameter of a sphere x^2+y^2+z^2-4x-2y+2z-30=0 is (4,5...

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  9. Find the equation of the sphere on the join of (2,3,5) and (4,9,-3) as...

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  10. If the vectors a^rarr=2overset^j-3overset^k and b^rarr=2overset^j+aove...

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  11. If |alphaoversetrarra|=2, what is the value of alpha?

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  12. If the position vectors of two points A ans B are 3overset^i+2overset^...

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  13. Given position vectors of P and Q, as (1,0,-2) and (3,-2,0) respective...

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  14. Given co-ordinates of the points A and B as (-1,-2) and (-5,-6) respec...

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  15. Write the unit vectors parallel to the vector 3overset^i+overset^j-2ov...

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  16. Find the direction cosines of the vectors, oversetrarr(r1)-oversetrarr...

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  17. Are the points A (2,6,3), B (1,2,7) and (3,10,-1) collinear?

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  18. What is the angle between the vectors oversetrarra=overset^i+overset^j...

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  19. What is the scalar product of the vectors oversetrarra=2overset^i+over...

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  20. What is the scalar projection of the vector oversetrarra=overset^i+ove...

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