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3D Geometry

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  1. 201.Consider the lines L_1: x-12=y-31=z-22 and L_2: x-21=y-22=z-33.
  2. 202.The distance of the point P(4,6,-2) from the line passing through the point (-3,2,3) and p…
  3. 203.Let the equation of the plane passing through the line x-2y-z-5=0=x+y+3z-5 and parallel to…
  4. 204.The foot of perpendicular of the point (2,0,5) on the line x+12=y-15=z+1-1 is (,,).
  5. 205.The shortest distance between the lines x+1=2y=-12z and x=y+2=6z-6 is:
  6. 206.If the shortest distance between the line joining the points (1,2,3) and (2,3,4), and the …
  7. 207.Let the coordinates of one vertex of ABC be A(0,2,), and the other two vertices lie on the…
  8. 208.Let the equation of the plane P containing the line x+10=8-y2=z be ax+by+3z=2(a+b), and th…
  9. 209.The plane 2x-y+z=4 intersects the line segment joining the points A(a,-2,4) and B(2,b,-3) …
  10. 210.If the lines x-11=y-22=z+31 and x-a2=y+23=z-31 intersect at the point P, then the distance…
  11. 211.Let a unit vector OP make angles ,, with the positive directions of the coordinate axes OX…
  12. 212.The line l_1 passes through the point (2,6,2) and is perpendicular to the plane 2x+y-2z=10…
  13. 213.If the equation of the plane passing through the point (1,1,2) and perpendicular to the li…
  14. 214.If _1<_2 are two values of such that the angle between the planes P_1: r(3 i-5 j+ k)=7 and…
  15. 215.If a plane passes through the points (-1,k,0), (2,k,-1), (1,1,2) and is parallel to the li…
  16. 216.Let a line L pass through the point P(2,3,1) and be parallel to the line of intersection o…
  17. 217.Let the shortest distance between the lines L: x-5-2=y-0=z+1, 0, and L_1: x+1=y-1=4-z be 2…
  18. 218.Let be the angle between the planes P_1: r( i+ j+2 k)=9 and P_2: r(2 i- j+ k)=15.
  19. 219.Let the line L: x-12=y+1-1=z-31 intersect the plane 2x+y+3z=16 at the point P.
  20. 220.If a point P(,,) satisfying [( )pmatrix2&10&89&3&88&4&8pmatrix=(0 0 0)] lies on the plane …
  21. 221.Let the plane P: 8x+_1y+_2z+12=0 be parallel to the line L: x+22=y-33=z+45.
  22. 222.The shortest distance between the lines x-51=y-22=z-4-3 and x+31=y+54=z-1-5 is:
  23. 223.Let the image of the point P(2,-1,3) in the plane x+2y-z=0 be Q.
  24. 224.Let the plane P pass through the intersection of the planes 2x+3y-z=2 and x+2y+3z=6, and b…
  25. 225.The point of intersection C of the plane 8x+y+2z=0 and the line joining the points A(-3,-6…
  26. 226.Let x+ y+ z=1 be the equation of a plane passing through the point (3,-2,5) and perpendicu…
  27. 227.If the equation of the plane passing through the line of intersection of the planes 2x-y+z…
  28. 228.If the equation of the plane containing the line x+2y+3z-4=0=2x+y-z+5 and perpendicular to…
  29. 229.Let _1,_2 be the values of for which the points (52,1,) and (-2,0,1) are at equal distance…
  30. 230.For a,b Z and |a-b|10, let the angle between the plane P: ax+y-z=b and the line x-1=a-y=z+…
  31. 231.Let O be the origin and the position vector of P be - i-2 j+3 k.
  32. 232.Let the image of the point P(1,2,6) in the plane passing through the points A(1,2,0), B(1,…
  33. 233.Let the line x1=6-y2=z+85 intersect the lines x-54=y-73=z+21 and x+36=3-y3=z-61 at the poi…
  34. 234.If the equation of the plane that contains the point (-2,3,5) and is perpendicular to each…
  35. 235.Let a line pass through the origin and be perpendicular to the lines _1: r=( i-11 j-7 k)+(…
  36. 236.Let the line : x=1-y-2=z-3, R, meet the plane P: x+2y+3z=4 at the point (,,).
  37. 237.Let the equation of the plane passing through the line of intersection of the planes x+2y+…
  38. 238.Let the image of the point (53,53,83) in the plane x-2y+z-2=0 be P.
  39. 239.If the line x=y=z intersects the line x A+y B+z C-18=0=x2A+y2B+z2C-9, where A,B,C are the …
  40. 240.Let the plane P contain the line 2x+y-z-3=0=5x-3y+4z+9 and be parallel to the line x+22=3-…
  41. 241.If the shortest distance between the lines x-12=y-23=z-3 and x-21=y-44=z-55 is 1√3, then t…
  42. 242.Let the points on the plane P be equidistant from the points (-4,2,1) and (2,-2,3).
  43. 243.Let Q be the mirror image of the point P(1,0,1) with respect to the plane S: x+y+z=5.
  44. 244.Let the lines L_1: r=( i+2 j+3 k), R, and L_2: r=( i+3 j+ k)+( i+ j+5 k), R, intersect at …
  45. 245.Let be the plane passing through the intersection of the planes r( i+3 j- k)=5 and r(2 i- …
  46. 246.Let l_1 be the line in the xy-plane with x- and y-intercepts 18 and 14√2 respectively, and…
  47. 247.If the two lines l_1: x-23=y+1-2, z=2 and l_2: x-11=2y+3=z+52 are perpendicular, then an a…
  48. 248.Let the plane 2x+3y+z+20=0 be rotated through a right angle about its line of intersection…
  49. 249.If the plane 2x+y-5z=0 is rotated about its line of intersection with the plane 3x-y+4z-7=…
  50. 250.If the lines r=( i- j+ k)+(3 j- k) and r=( i- j)+(2 i-3 k) are coplanar, then the distance…