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3D Geometry

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  1. 301.Let P be a plane passing through the points (1,0,1), (1,-2,1) and (0,1,-2).
  2. 302.Consider the line L given by x-32=y-11=z-21.
  3. 303.The angle between the straight lines, whose direction cosines are given by the equations 2…
  4. 304.The square of the distance of the point of intersection of the line x-12=y-23=z+16 and the…
  5. 305.The distance of the point (-1,2,-2) from the line of intersection of the planes 2x+3y+2z=0…
  6. 306.If the equation of plane passing through the mirror image of a point (2,3,1) with respect …
  7. 307.Suppose the line x-2=y-2-5=z+22 lies on the plane x+3y-2z+=0.
  8. 308.Let the equation of the plane, that passes through the point (1,4,-3) and contains the lin…
  9. 309.The distance of the point (1,-2,3) from the plane x-y+z=5 measured parallel to a line, who…
  10. 310.Equation of a plane at a distance 221 from the origin, which contains the line of intersec…
  11. 311.The equation of the plane passing through the line of intersection of the planes r( i+ j+ …
  12. 312.Let S be the mirror image of the point Q(1,3,4) with respect to the plane 2x-y+z+3=0 and l…
  13. 313.A plane P contains the line x+2y+3z+1=0=x-y-z-6 and is perpendicular to the plane -2x+y+z+…
  14. 314.Let P be the plane passing through the point (1,2,3) and the line of intersection of the p…
  15. 315.Let the line L be the projection of the line x-12=y-31=z-42 in the plane x-2y-z=3.
  16. 316.Let Q be the foot of the perpendicular from the point P(7,-2,13) on the plane containing t…
  17. 317.The distance of line 3y-2z-1=0=3x-z+4 from the point (2,-1,6) is
  18. 318.Let the acute angle bisector of the two planes x-2y-2z+1=0 and 2x-3y-6z+1=0 be the plane P…
  19. 319.The shortest distance between the lines x-33=y-8-1=z-31 and x+3-3=y+72=z-64 is:
  20. 320.If the foot of the perpendicular drawn from the point (1,0,3) on a line passing through (,…
  21. 321.If for some and in R, the intersection of the following three planes [x+4y-2z=1, x+7y-5z=,…
  22. 322.If the distance between the plane 23x-10y-2z+48=0 and the plane containing the lines x+12=…
  23. 323.The mirror image of the point (1,2,3) in a plane is (-73,-43,-13).
  24. 324.Let P be a plane passing through the points (2,1,0), (4,1,1) and (5,0,1) and R be any poin…
  25. 325.A plane P meets the coordinate axes at A, B and C respectively.
  26. 326.If (a,b,c) is the image of the point (1,2,-3) in the line x+12=y-3-2=z-1, then a+b+c is eq…
  27. 327.The lines r= i- j+l(2 i+ k) and r=2 i- j+m( i+ j- k):
  28. 328.The shortest distance between the lines x-10=y+1-1=z1 and x+y+z+1=0, 2x-y+z+3=0 is:
  29. 329.If for some R, the lines L_1:x+12=y-2-1=z-11 and L_2:x+2=y+15-=z+11 are coplanar, then the…
  30. 330.If the equation of a plane P, passing through the intersection of the planes x+4y-z+7=0 an…
  31. 331.The distance of the point (1,-2,3) from the plane x-y+z=5 measured parallel to the line x2…
  32. 332.The foot of the perpendicular drawn from the point (4,2,3) to the line joining the points …
  33. 333.The plane which bisects the line joining the points (4,-2,3) and (2,4,-1) at right angles …
  34. 334.Let a plane P contain two lines r= i+( i+ j), R, and r=- j+( j- k), R.
  35. 335.The plane passing through the points (1,2,1), (2,1,2) and parallel to the line, 2x=3y, z=1…
  36. 336.A plane passing through the point (3,1,1) contains two lines whose direction ratios are 1,…
  37. 337.Let S be the set of all real values of such that a plane passing through the points (-^2,1…
  38. 338.The plane containing the line x-32=y+2-1=z-13 and also containing its projection on the pl…
  39. 339.The direction ratios of normal to the plane through the points (0,-1,0) and (0,0,1) and ma…
  40. 340.If the point (2,,) lies on the plane which passes through the points (3,4,2) and (7,0,6) a…
  41. 341.The plane which bisects the line segment joining the points (-3,-3,4) and (3,7,6) at right…
  42. 342.On which of the following lines lies the point of intersection of the line x-42=y-52=z-31 …
  43. 343.The system of linear equations [x+y+z=2, 2x+3y+2z=5, 2x+3y+(a^2-1)z=a+1]
  44. 344.The equation of the line passing through (-4,3,1), parallel to the plane x+2y-z-5=0 and in…
  45. 345.The plane through the intersection of the planes x+y+z=1 and 2x+3y-z+4=0 and parallel to t…
  46. 346.The equation of the plane containing the straight line x2= y3= z4 and perpendicular to the…
  47. 347.A tetrahedron has vertices P(1,2,1), Q(2,1,3), R(-1,1,2) and O(0,0,0).
  48. 348.Two lines x-31=y+13=z-6-1 and x+57=y-2-6=z-34 intersect at the point R.
  49. 349.If the lines x=ay+b, z=cy+d and x=a'z+b', y=c'z+d' are perpendicular, then:
  50. 350.The perpendicular distance from the origin to the plane containing the two lines, x+23=y-2…