CBSE  /  Class 12  /  Maths  /  Three Dimensional Geometry

  • 1. 
    If a line makes angles α, β, γ with the axis then cos 2α + cos 2β + cos 2γ =

  • -2
  • -1
  • 1
  • 2

  • 2. 
    The line x = 1, y = 2 is

  • parallel to x-axis
  • parallel to y-axis
  • parallel to z-axis
  • None of these

  • 3. 
    The points A (1, 1, 0), B(0, 1, 1), C(1, 0, 1) and D(\(\frac{2}{3}\), \(\frac{2}{3}\), \(\frac{2}{3}\))

  • Coplanar
  • Non-coplanar
  • Vertices of a parallelogram
  • None of these

  • 4. 
    The angle between the planes 2x – y + z = 6 and x + y + 2z = 7 is

  • \(\frac{π}{4}\)
  • \(\frac{π}{6}\)
  • \(\frac{π}{3}\)
  • \(\frac{π}{2}\)

  • 5. 
    The distance of the points (2, 1, -1) from the plane x- 2y + 4z – 9 is

  • \(\frac{\sqrt{31}}{21}\)
  • \(\frac{13}{21}\)
  • \(\frac{13}{\sqrt{21}}\)
  • \(\sqrt{\frac{π}{2}}\)

  • 6. 
    The planes \(\vec{r}\)(2\(\hat{i}\) + 3\(\hat{j}\) – 6\(\hat{k}\)) = 7 and

  • parallel
  • at right angles
  • equidistant front origin
  • None of these

  • 7. 
    The equation of the plane through point (1, 2, -3) which is parallel to the plane 3x- 5y + 2z = 11 is given by

  • 3x – 5y + 2z – 13 = 0
  • 5x – 3y + 2z + 13 = 0
  • 3x – 2y + 5z + 13 = 0
  • 3x – 5y + 2z + 13 = 0

  • 8. 
    Distance of the point (a, β, γ) from y-axis is

  • β
  • |β|
  • |β + γ|
  • \(\sqrt{α^2+γ^2}\)

  • 9. 
    If the directions cosines of a line are A, k, k, then

  • k > 0
  • 0 < k < 1
  • k = 1
  • k = \(\frac{1}{√3}\) or –\(\frac{1}{√3}\)

  • 10. 
    The distance of the plane \(\vec{r}\)(\(\frac{-2}{7}\)\(\hat{i}\) – \(\frac{3}{7}\)\(\hat{j}\) + \(\frac{6}{7}\)\(\hat{k}\)) = 0 from the orgin is

  • 1
  • 7
  • \(\frac{1}{7}\)
  • None of these
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