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3D Geometry

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  1. 151.Let the image of the point P(0,-5,0) in the line x-12=y1=z+1-2 be the point R, and the ima…
  2. 152.Let the line L pass through the point (-3,5,2) and make equal angles with the positive coo…
  3. 153.Let P(,,) be the point on the line x-12=y+1-3=z1 at a distance 4√14 from the point (1,-1,0…
  4. 154.Let L be the line x+12=y+13=z+36 and let S be the set of all points (a,b,c) on L whose dis…
  5. 155.The vertices B and C of a triangle ABC lie on the line x1=1-y-2=z-23.
  6. 156.Let the direction cosines of two lines satisfy the equations 4l+m-n=0 and 2mn+10nl+3lm=0.
  7. 157.The sum of all values of , for which the shortest distance between the lines [L_1: r=- i+2…
  8. 158.If the distances of the point (1,2,a) from the line L: x-11=y2=z-11, measured along the li…
  9. 159.Let Q(a,b,c) be the image of the point P(3,2,1) in the line L_1: x-11=y2=z-11.
  10. 160.Let a line L passing through the point (1,1,1) be perpendicular to two given vectors whose…
  11. 161.Let the point A be the foot of perpendicular drawn from the point P(a,b,0) on the line x-1…
  12. 162.The square of the distance of the point P(-2,-8,6) from the line L_1: x-11=y-12=z-1, measu…
  13. 163.A line with direction ratios (1,-1,2) intersects the lines L_1: x2=y3=z+13 and L_2: x+1-1=…
  14. 164.If B is the image of A(,2,1) in the line x-23=y-12=z1, and B=(2+1, ^2-3, -12), then the po…
  15. 165.The shortest distance between the lines [ r=(13 i+2 j+83 k)+(2 i-5 j+6 k) and r=(-23 i-13 …
  16. 166.The lines r_1=( i+ j- k)+(a i- j), a0, and r_2=(4 i- k)+(2 i+a k) intersect.
  17. 167.Let a line L be perpendicular to both the lines L_1: x+13=y+35=z+57 and L_2: x-21=y-44=z-6…
  18. 168.Let the area of the triangle formed by the lines L_1: x+2=y-1=z, L_2: x-35=y-1=z-11, and L…
  19. 169.Let in a ABC, the length of the side AC be 6, the vertex B be (1,2,3), and the vertices A,…
  20. 170.Let the line passing through the points (-1,2,1) and parallel to the line x-12=y+13=z4 int…
  21. 171.Let A(x,y,z) be a point in the xy-plane which is equidistant from the three points (0,3,2)…
  22. 172.Let L_1: x-11=y-2-1=z-12 and L_2: x+1-1=y-22=z1 be two lines.
  23. 173.Let a straight line L pass through the point P(2,-1,3) and be perpendicular to the lines x…
  24. 174.Let ABCD be a tetrahedron such that the edges AB, AC and AD are mutually perpendicular.
  25. 175.Line L_1 passes through the point (1,2,3) and is parallel to the z-axis.
  26. 176.Each of the angles and that a given line makes with the positive y- and z-axes, respective…
  27. 177.Let A and B be two distinct points on the line L: x-63=y-72=z-7-2.
  28. 178.Let the shortest distance between the lines L_1: x-33=y--1=z-31 and L_2: x+3-3=y+72=z-4 be…
  29. 179.Let the values of p, for which the shortest distance between the lines x+13=y4=z5 and r=(p…
  30. 180.Consider the lines L_1: x-1=y-2=z and L_2: x-2=y=z-1.
  31. 181.If the equation of the line passing through the point (0,-12,0) and perpendicular to the l…
  32. 182.The position vectors of the vertices A,B,C of a triangle are 2 i-3 j+3 k, 2 i+2 j+3 k, and…
  33. 183.Let the position vectors of the vertices A,B,C of a triangle be 2 i+2 j+ k, i+2 j+2 k, and…
  34. 184.Let the image of the point (1,0,7) in the line x1=y-12=z-23 be the point (,,).
  35. 185.The lines x-22=y-2=z-716 and x+34=y+23=z+21 intersect at the point P.
  36. 186.Let O be the origin and the position vectors of A and B be 2 i+2 j+ k and 2 i+4 j+4 k resp…
  37. 187.A line with direction ratios 2,1,2 meets the lines x=y+2=z and x+2=2y=2z at the points P a…
  38. 188.Let P(3,2,3), Q(4,6,2), R(7,3,2) be the vertices of PQR.
  39. 189.Let a line passing through the point (-1,2,3) intersect the lines L_1: x-13=y-22=z+1-2 at …
  40. 190.The distance of the point Q(0,2,-2) from the line passing through the point P(5,-4,3) and …
  41. 191.Let Q and R be the feet of perpendiculars from the point P(a,a,a) on the lines x=y, z=1 an…
  42. 192.The shortest distance between lines L_1 and L_2, where L_1: x-12=y+1-3=z+42 and L_2 is the…
  43. 193.A line passes through A(4,-6,-2) and B(16,-2,4).
  44. 194.Let the line of the shortest distance between the lines L_1: r=( i+2 j+3 k)+( i- j+ k) and…
  45. 195.The distance of the point (-1,9,-16) from the plane 2x+3y-z=5, measured parallel to the li…
  46. 196.The distance of the point (7,-3,-4) from the plane passing through the points (2,-3,1), (-…
  47. 197.The shortest distance between the lines x-23=y+12=z-62 and x-63=1-y2=z+80 is equal to: Ans…
  48. 198.If the foot of the perpendicular drawn from (1,9,7) to the line passing through the point …
  49. 199.Let the plane containing the line of intersection of the planes P_1: x+(+4)y+z=1 and P_2: …
  50. 200.If the shortest distance between the lines x+√62=y-√63=z-√64 and x-3=y-2√64=z+2√65 is 6, t…