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3D Geometry

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  1. 351.If an angle between the line x+12=y-21=z-3-2 and the plane x-2y-kz=3 is ^-12√23, then a va…
  2. 352.If the length of the perpendicular from the point (,0,) (0) to the line x1=y-10=z+1-1 is 3…
  3. 353.The vertices B and C of a ABC lie on the line x+23=y-10= z4 such that BC=5 units.
  4. 354.If a point R(4,y,z) lies on the line segment joining the points P(2,-3,4) and Q(8,0,10), t…
  5. 355.A perpendicular is drawn from a point on the line x-12=y+1-1= z1 to the plane x+y+z=3 such…
  6. 356.The length of the perpendicular from the point (2,-1,4) on the straight line x+310=y-2-7= …
  7. 357.If the line x-23=y+12=z-1-1 intersects the plane 2x+3y-z+13=0 at a point P and the plane 3…
  8. 358.A plane which bisects the angle between the two given planes 2x-y+2z-4=0 and x+2y+2z-2=0, …
  9. 359.The length of the perpendicular drawn from the point (2,1,4) to the plane containing the l…
  10. 360.If Q(0,-1,-3) is the image of the point P in the plane 3x-y+4z=2 and R is the point (3,-1,…
  11. 361.If the plane 2x-y+2z+3=0 has the distances 13 and 23 units from the planes 4x-2y+4z+=0 and…
  12. 362.If the line x-12=y+13=z-24 meets the plane x+2y+3z=15 at a point P, then the distance of P…
  13. 363.A plane passing through the points (0,-1,0) and (0,0,1) and making an angle 4 with the pla…
  14. 364.Let P be the plane which contains the line of intersection of the planes x+y+z-6=0 and 2x+…
  15. 365.The equation of a plane containing the line of intersection of the planes 2x-y-4=0 and y+2…
  16. 366.The vector equation of the plane through the line of intersection of the planes x+y+z=1 an…
  17. 367.The length of the projection of the line segment joining the points (5,-1,4) and (4,-1,3) …
  18. 368.An angle between the lines whose direction cosines are given by the equations l+3m+5n=0 an…
  19. 369.If the angle between the lines x2= y2= z1 and 5-x-2=7y-14P=z-34 is ^-123, then P is equal …
  20. 370.If L_1 is the line of intersection of the planes 2x-2y+3z-2=0, x-y+z+1=0, and L_2 is the l…
  21. 371.A variable plane passes through a fixed point (3,2,1) and meets the x,y,z axes at A,B,C re…
  22. 372.An angle between the plane x+y+z=5 and the line of intersection of the planes 3x+4y+z-1=0 …
  23. 373.A plane bisects the line segment joining the points (1,2,3) and (-3,4,5) at right angles.
  24. 374.If the image of the point P(1,-2,3) in the plane 2x+3y-4z+22=0 measured parallel to line x…
  25. 375.The distance of the point (1,3,-7) from the plane passing through the point (1,-1,-1), hav…
  26. 376.If x=a,y=b,z=c is a solution of the system of linear equations [x+8y+7z=0, 9x+2y+3z=0, x+y…
  27. 377.If a variable plane, at a distance of 3 units from the origin, intersects the coordinate a…
  28. 378.If the line x-31=y+2-1=z+-2 lies in the plane 2x-4y+3z=2, then the shortest distance betwe…
  29. 379.The coordinates of the foot of the perpendicular from the point (1,-2,1) on the plane cont…
  30. 380.The line of intersection of the planes r(3 i- j+ k)=1 and r( i+4 j-2 k)=2, is:
  31. 381.ABC is a triangle in a plane with vertices A(2,3,5), B(-1,3,2) and C(,5,).
  32. 382.The number of distinct real values of for which the lines x-11=y-22=z+3^2 and x-31=y-2=z-1…
  33. 383.If the line x-32=y+2-1=z+43 lies in the plane lx+my-z=9, then l^2+m^2 is equal to:
  34. 384.The distance of the point (1,-5,9) from the plane x-y+z=5 measured along the straight line…
  35. 385.The distance of the point (1,-2,4) from the plane passing through the point (1,2,2) and pe…
  36. 386.The equation of the plane containing the line 2x-5y+z=3, x+y+4z=5, and parallel to the pla…
  37. 387.The distance of the point (1,0,2) from the point of intersection of the line x-23=y+14=z-2…
  38. 388.The shortest distance between the z-axis and the line x+y+2z-3=0=2x+3y+4z-4, is
  39. 389.A plane containing the point (3,2,0) and the line x-11=y-25=z-34 also contains the point:
  40. 390.If the points (1,1,) and (-3,0,1) are equidistant from the plane 3x+4y-12z+13=0, then sati…
  41. 391.If the shortest distance between the lines x-1=y+1-1= z1 (-1) and x+y+z+1=0=2x-y+z+3 is 1√…
  42. 392.The angle between the lines whose direction cosines satisfy the equations l+m+n=0 and l^2=…
  43. 393.Let A(2,3,5), B(-1,3,2) and C(,5,) be the vertices of a ABC.
  44. 394.A line in 3-dimensional space makes an angle (0</2) with both the x and y axes.
  45. 395.Equation of the line of the shortest distance between the lines x1= y-1= z1 and x-10=y+1-2…
  46. 396.The image of the line x-13=y-31=z-4-5 in the plane 2x-y+z+3=0 is the line:
  47. 397.If the angle between the line 2(x+1)=y=z+4 and the plane 2x-y+ z+4=0 is 6, then the value …
  48. 398.If the distance between planes 4x-2y-4z+1=0 and 4x-2y-4z+d=0 is 7, then d is:
  49. 399.A symmetrical form of the line of intersection of the planes x=ay+b and z=cy+d is
  50. 400.The plane containing the line x-11=y-22=z-33 and parallel to the line x1= y1= z4 passes th…