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3D Geometry

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  1. 1.Let the foot of perpendicular from the point ( ,2,3) on the line (x-4)/(1)=(y-9)/(2)=(z-5)…
  2. 2.The shortest distance between the lines (x-4)/(1)=(y-3)/(2)=(z-2)/(-3) and (x+2)/(2)=(y-6)…
  3. 3.Let the image of the point P(1,6,a) in the line L:(x)/(1)=(y-1)/(2)=(z-a+1)/(b),b>0, be ((…
  4. 4.Let a line L be perpendicular to both the lines L_1:(x+1)/(3)=(y+3)/(5)=(z+5)/(7) and L_2:…
  5. 5.Let a triangle PQR be such that P and Q lie on the line (x+3)/(8)=(y-4)/(2)=(z+1)/(2) and …
  6. 6.If the distance of the point (a, 2,5) from the image of the point (1,2,7) in the line (x)/…
  7. 7.The square of the distance of the point P(5,6,7) from the line (x-2)/(2)=(y-5)/(3)=(z-2)/(…
  8. 8.r=(i+j-k)+ (ai-j),a 0 and r=(4i-k)+ (2i+ak) from the origin is :
  9. 9.The shortest distance between the lines r=((1)/(3)i+2j+(8)/(3)k)+ (2i-5j+6k) and r=(-(2)/(…
  10. 10.If (2 +1, ^2-3 ,( -1)/(2)) is the image of ( ,2 ,1) in the line (x-2)/(3)=(y-1)/(2)=(z)/(1…
  11. 11.A line with direction ratios 1,-1,2 intersects the lines (x)/(2)=(y)/(3)=(z+1)/(3) and (x+…
  12. 12.The square of the distance of the point (-2,-8,6) from the line (x-1)/(1)=(y-1)/(2)=(z)/(-…
  13. 13.Let the point A be the foot of perpendicular drawn from the point P(a, b, 0) on the line[(…
  14. 14.If the point of intersection of the lines (x+1)/(3) = (y+a)/(5) = (z+b+1)/(7) and (x-2)/(1…
  15. 15.Let a line L passing through the point (1, 1, 1) be perpendicular to both the vectors 2i +…
  16. 16.Let Q(a, b, c) be the image of the point P(3, 2, 1) in the line (x-1)/(1) = (y)/(2) = (z-1…
  17. 17.If the distances of the point (1,2, a) from the line (x-1)/(1)=(y)/(2)=(z-1)/(1) along the…
  18. 18.The sum of all values of , for which the shortest distance between the lines (x+1)/( )=(y-…
  19. 19.Let the direction cosines of two lines satisfy the equations : 4 l+m-n=0 and 2 m n+10 n l+…
  20. 20.The vertices B and C of a triangle ABC lie on the line (x)/(1)=(1-y)/(-2)=(z-2)/(3).
  21. 21.Let L be the line (x+1)/(2)=(y+1)/(3)=(z+3)/(6) and let S be the set of all points (a, b, …
  22. 22.Let P( , , ) be the point on the line (x-1)/(2)=(y+1)/(-3)=z at a distance 4√14 from the p…
  23. 23.If the image of the point P(1,2,a) in the line (x-6)/(3)=(y-7)/(2)=(7-z)/(2) is Q(5,b,c), …
  24. 24.Let the line L pass through the point (-3, 5, 2) and make equal angles with the positive c…
  25. 25.Let the line L_1 be parallel to the vector -3i+2j+4k and pass through the point (2,6,7), a…
  26. 26.Let the values of for which the shortest distance between the lines (x-1)/(2)=(y-2)/(3)=(z…
  27. 27.If the equation of the line passing through the point (0,-(1)/(2),0) and perpendicular to …
  28. 28.Consider the lines L1: x - 1 = y - 2 = z and L2: x - 2 = y = z - 1.
  29. 29.Let the line L pass through (1,1,1) and intersect the lines (x-1)/(2)=(y+1)/(3)=(z-1)/(4) …
  30. 30.If the shortest distance between the lines (x-1)/(2)=(y-2)/(3)=(z-3)/(4) and (x)/(1)=(y)/(…
  31. 31.Let A be the point of intersection of the lines L_1:(x-7)/(1)=(y-5)/(0)=(z-3)/(-1) and L_2…
  32. 32.Let the values of p , for which the shortest distance between the lines (x+1)/(3)=(y)/(4)=…
  33. 33.Let the shortest distance between the lines (x-3)/(3)=(y- )/(-1)=(z-3)/(1) and (x+3)/(-3)=…
  34. 34.Let A and B be two distinct points on the line L: (x-6)/(3)=(y-7)/(2)=(z-7)/(-2).
  35. 35.Each of the angles and that a given line makes with the positive y - and z-axes, respectiv…
  36. 36.The distance of the point (7,10,11) from the line (x-4)/(1)=(y-4)/(0)=(z-2)/(3) along the …
  37. 37.Let a line passing through the point (4,1,0) intersect the line L_1:(x-1)/(2)=(y-2)/(3)=(z…
  38. 38.Line L_1 passes through the point (1,2,3) and is parallel to z-axis.
  39. 39.If the image of the point P(1,0,3) in the line joining the points A(4,7,1) and B(3,5,3) is…
  40. 40.The line L_1 is parallel to the vector a=-3i+2j+4k and passes through the point (7,6,2) an…
  41. 41.Let the vertices Q and R of the triangle PQR lie on the line (x+3)/(5)=(y-1)/(2)=(z+4)/(3)…
  42. 42.Let A B C D be a tetrahedron such that the edges A B, A C and A D are mutually perpendicul…
  43. 43.Let a straight line L pass through the point P(2, -1, 3) and be perpendicular to the lines…
  44. 44.Let P be the foot of the perpendicular from the point (1,2,2) on the line L:(x-1)/(1)=(y+1…
  45. 45.Let L_1:(x-1)/(1)=(y-2)/(-1)=(z-1)/(2) and L_2:(x+1)/(-1)=(y-2)/(2)=(z)/(1) be two lines.
  46. 46.The square of the distance of the point ((15)/(7),(32)/(7),7) from the line (x+1)/(3)=(y+3…
  47. 47.Let A(x,y,z) be a point in xy-plane, which is equidistant from three points (0,3,2),(2,0,3…
  48. 48.If the image of the point (4,4,3) in the line (x-1)/(2)=(y-2)/(1)=(z-1)/(3) is ( , , ), th…
  49. 49.Let in a A B C, the length of the side A C be 6 , the vertex B be (1,2,3) and the vertices…
  50. 50.Let the line passing through the points (-1,2,1) and parallel to the line (x-1)/(2)=(y+1)/…