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3D Geometry

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  1. 401.Equation of the plane which passes through the point of intersection of lines x-13=y-21=z-…
  2. 402.Let ABC be a triangle with vertices at points A(2,3,5), B(-1,3,2) and C(,5,) in three-dime…
  3. 403.If the projections of a line segment on the x, y and z-axes in 3-dimensional space are 2, …
  4. 404.The acute angle between two lines such that the direction cosines l,m,n of each of them sa…
  5. 405.If the lines x-21=y-31=z-4-k and x-1k=y-42=z-51 are coplanar, then k can have
  6. 406.If two lines L_1 and L_2 in space are defined by L_1=x= y+(-1), z=(-1)y+ and L_2=x= y+(1-)…
  7. 407.If the lines x+12=y-11=z+13 and x+22=y-k3= z4 are coplanar, then the value of k is:
  8. 408.Distance between two parallel planes 2x+y+2z=8 and 4x+2y+4z+5=0 is
  9. 409.The equation of a plane through the line of intersection of the planes x+2y=3, y-2z+1=0, a…
  10. 410.Let Q be the foot of perpendicular from the origin to the plane 4x-3y+z+13=0 and R be the …
  11. 411.A vector n is inclined to the x-axis at 45^, to the y-axis at 60^ and at an acute angle to…
  12. 412.If the line x-12=y+13=z-14 and x-31=y-k2= z1 intersect, then k is equal to:
  13. 413.The distance of the point - i+2 j+6 k from the straight line that passes through the point…
  14. 414.Statement 1: The shortest distance between the lines x2= y-1= z2 and x-14=y-1-2=z-14 is √2…
  15. 415.The coordinates of the foot of perpendicular from the point (1,0,0) to the line x-12=y+1-3…
  16. 416.An equation of a plane parallel to the plane x-2y+2z-5=0 and at a unit distance from the o…
  17. 417.The equation of a plane containing the line x+1-3=y-32=z+21 and the point (0,7,-7) is
  18. 418.Consider the following planes: [P: x+y-2z+7=0, Q: x+y+2z+2=0, R: 3x+3y-6z-11=0.]
  19. 419.If the three planes x=5, 2x-5ay+3z-2=0 and 3bx+y-3z=0 contain a common line, then (a,b) is…
  20. 420.A line with positive direction cosines passes through the point P(2,-1,2) and makes equal …
  21. 421.The values of a for which the two points (1,a,1) and (-3,0,a) lie on the opposite sides of…
  22. 422.The length of the perpendicular drawn from the point (3,-1,11) to the line x2=y-23=z-34 is…
  23. 423.Statement-1: The point A(1,0,7) is the mirror image of the point B(1,6,3) in the line x1=y…
  24. 424.If the angle between the line x=y-12=z-3 and the plane x+2y+3z=4 is ^-1514, then equals
  25. 425.A line AB in three-dimensional space makes angles 45^ and 120^ with the positive x-axis an…
  26. 426.The line L given by x5+ yb=1 passes through the point (13,32).
  27. 427.Statement-1: The point A(3,1,6) is the mirror image of the point B(1,3,4) in the plane x-y…
  28. 428.The projections of a vector on the three coordinate axes are 6,-3,2 respectively.
  29. 429.Let the line x-23=y-1-5=z+22 lie in the plane x+3y- z+=0.
  30. 430.If the straight lines x-1k=y-22=z-33 and x-23=y-3k=z-12 intersect at a point, then the int…
  31. 431.The line passing through the points (5,1,a) and (3,b,1) crosses the yz-plane at the point …
  32. 432.If a line makes an angle of /4 with the positive directions of each of the x-axis and y-ax…
  33. 433.Let L be the line of intersection of the planes 2x+3y+z=1 and x+3y+2z=2.
  34. 434.*Topic: Sphere and Miscellaneous Problems on Sphere* If (2,3,5) is one end of a diameter o…
  35. 435.The image of the point (-1,3,4) in the plane x-2y=0 is
  36. 436.If non-zero numbers a,b,c are in H.P., then the straight line xa+ yb+1c=0 always passes th…
  37. 437.The angle between the lines 2x=3y=-z and 6x=-y=-4z is
  38. 438.The distance between the line r=2 i-2 j+3 k+( i- j+4 k) and the plane r( i+5 j+ k)=5 is
  39. 439.If the angle between the line x+11=y-12=z-22 and the plane 2x-y+ z+4=0 is such that =13, t…
  40. 440.The plane x+2y-z=4 cuts the sphere x^2+y^2+z^2-x+z-2=0 in a circle of radius
  41. 441.If the plane 2ax-3ay+4az+6=0 passes through the mid-point of the line joining the centres …
  42. 442.A line makes the same angle with each of the x and z axes.
  43. 443.If the straight lines x=1+s, y=-3- s, z=1+ s and x= t2, y=1+t, z=2-t, with parameters s an…
  44. 444.A line with direction cosines proportional to 2,1,2 meets each of the lines x=y+a=z and x+…
  45. 445.The intersection of the spheres x^2+y^2+z^2+7x-2y-z=13 and x^2+y^2+z^2-3x+3y+4z=8 is the s…
  46. 446.The two lines x=ay+b, z=cy+d and x=a'y+b', z=c'y+d' will be perpendicular, if and only if
  47. 447.Two systems of rectangular axes have the same origin.
  48. 448.The radius of the circle in which the sphere x^2+y^2+z^2+2x-2y-4z-19=0 is cut by the plane…
  49. 449.The shortest distance from the plane 12x+4y+3z=327 to the sphere x^2+y^2+z^2+4x-2y-6z=155 …
  50. 450.The direction ratios of the normal to the plane through (1,0,0), (0,1,0), which makes an a…