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Most Important Selected Qs for JEE AdvancedMathematicsThree Dimensional Geometry

A rod of length 2 units whose one end is (1,0,-1) and other end touches the plane x-2 y+2 z+4=0 , is rotated on this plane, then

Options

  1. Athe rod sweeps a solid structure whose volume is cubic units
  2. Bthe area of the region which the rod traces on the plane is 2
  3. Cthe length of projection of the rod on the plane is 3 units
  4. Dthe centre of the region which the rod traces on the plane is ( 2 3 , 2 3 , -5 3 )

Correct answer

D. the centre of the region which the rod traces on the plane is ( 2 3 , 2 3 , -5 3 )

Step-by-step solution

The rod sweeps out the figure which is a cone. The distance of point (A(1,0,-1) from the plane is 1+1-2+4 9 =1 unit. The slant height / of the cone is 2 units. Then the radius of the base of the cone is l^2-1 = 4-1 = 3 Hence, the volume of the cone is 3 ( 3 )^2 .1= cubic units. Area of the circle on the plane which the rod traces is 3 . Also, the centre of the circle is Q(x, y, z) . Then aligned & x-1 1 = y-0 -2 = z+1 2 = -(1-0-2+4) 1^2+(-2)^2+2^2 & Q(x, y, z) ( 2 3 , 2 3 , -5 3 ) aligned

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