Engineering Board Exam Reviewer · Solid Analytic Geometry · hard

Find the radius of the sphere with center (1,-2,3) that is tangent to the plane 2x-y+2z-3=0.

  1. 10/3
  2. 7
  3. 7/3
  4. 13/3

Answer

C. 7/3

Solution

The radius is the distance from the center to the plane: r= |2(1)-(-2)+2(3)-3|sqrt(4+1+4)=7/3 2.33.

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  2. Find the angle between two lines with direction numbers (1,1,0) and (0,1,1), in degrees.
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  5. Find the acute angle between the planes x+y+z=3 and x-y+z=5, in degrees.
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