CBSE  /  Class 11  /  Maths  /  Introduction to Three Dimensional Geometry

  • 1. 
    The coordinates of the point where the line through (5, 1, 6) and (3, 4, 1) crosses the YZ plane is

  • (0, 17/2, 13/2)
  • (0, -17/2, -13/2)
  • (0, 17/2, -13/2)
  • None of these

  • 2. 
    The angle between the vectors with direction ratios are 4, -3, 5 and 3, 4, 5 is

  • π/2
  • π/3
  • π/4
  • π/6

  • 3. 
    The equation of plane passing through the point i + j + k and parallel to the plane r . (2i – j + 2k) = 5 is

  • r . (2i – j + 2k) = 2
  • r . (2i – j + 2k) = 3
  • r . (2i – j + 2k) = 4
  • r . (2i – j + 2k) = 5

  • 4. 
    A vector r is equally inclined with the coordinate axes. If the tip of r is in the positive octant and |r| = 6, then r is

  • 2√3(i – j + k)
  • 2√3(-i + j + k)
  • 2√3(i + j – k)
  • 2√3(i + j + k)

  • 5. 
    The maximum distance between points (3sin θ, 0, 0) and (4cos θ, 0, 0) is

  • 3
  • 4
  • 5
  • Can not be find

  • 6. 
    The image of the point P(1, 3, 4) in the plane 2x – y + z = 0 is

  • (-3, 5, 2)
  • (3, 5, 2)
  • (3, -5, 2)
  • (3, 5, -2)

  • 7. 
    The points on the y- axis which are at a distance of 3 units from the point (2, 3, -1) is

  • either (0, -1, 0) or (0, -7, 0)
  • either (0, 1, 0) or (0, 7, 0)
  • either (0, 1, 0) or (0, -7, 0)
  • either (0, -1, 0) or (0, 7, 0)

  • 8. 
    If α, β, γ are the angles made by a half ray of a line respectively with positive directions of X-axis Y-axis and Z-axis, then sin² α + sin² β + sin² γ =

  • 1
  • 0
  • -1
  • None of these

  • 9. 
    If P(x, y, z) is a point on the line segment joining Q(2, 2, 4) and R(3, 5, 6) such that the projections of OP on the axes are 13/5, 19/5, 26/5 respectively, then P divides QR in the ration

  • 1 : 2
  • 3 : 2
  • 2 : 3
  • 1 : 3

  • 10. 
    In a three dimensional space, the equation 3x – 4y = 0 represents

  • a plane containing Y axis
  • none of these
  • a plane containing Z axis
  • a plane containing X axis
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