CBSE  /  Class 12  /  Maths  /  Three Dimensional Geometry

  • 1. 
    The coordinates of the midpoints of the line segment joining the points (2, 3, 4) and (8, -3, 8) are

  • (10, 0, 12)
  • (5, 6, 0)
  • (6, 5, 0)
  • (5, 0, 6)

  • 2. 
    The direction cosines of the normal to the plane 2x – 3y – 6z – 3 = 0 are

  • \(\frac{2}{7}\), \(\frac{-3}{7}\), \(\frac{-6}{7}\)
  • \(\frac{2}{7}\), \(\frac{3}{7}\), \(\frac{6}{7}\)
  • \(\frac{-2}{7}\), \(\frac{-3}{7}\), \(\frac{-6}{7}\)
  • None of these

  • 3. 
    If 2x + 5y – 6z + 3 = 0 be the equation of the plane, then the equation of any plane parallel to the given plane is

  • 3x + 5y – 6z + 3 = 0
  • 2x – 5y – 6z + 3 = 0
  • 2x + 5y – 6z + k = 0
  • None of these

  • 4. 
    (2, – 3, – 1) 2x – 3y + 6z + 7 = 0

  • 4
  • 3
  • 2
  • \(\frac{1}{5}\)

  • 5. 
    The length of the ⊥

  • 0
  • 2√3
  • \(\frac{2}{3}\)
  • 2

  • 6. 
    The shortest distance between the lines \(\vec{r}\) = \(\vec{a}\) + k\(\vec{b}\) and r = \(\vec{a}\) + l\(\vec{c}\) is (\(\vec{b}\) and \(\vec{c}\) are non-collinear)

  • 0
  • |\(\vec{b}\).\(\vec{c}\)|
  • \(\frac{|\vec{b}×\vec{c}|}{|\vec {a}|}\)
  • \(\frac{|\vec{b}.\vec{c}|}{|\vec {a}|}\)

  • 7. 
    The equation xy = 0 in three dimensional space is represented by

  • a plane
  • two plane are right angles
  • a pair of parallel planes
  • a pair of st. line

  • 8. 
    The direction cosines of any normal to the xy plane are

  • 1, 0 ,0
  • 0, 1, 0
  • 1, 1, 0
  • 1, 1, 0

  • 9. 
    How many lines through the origin in make equal angles with the coordinate axis?

  • 1
  • 4
  • 8
  • 2

  • 10. 
    The direction cosines of the line joining (1, -1, 1) and (-1, 1, 1) are

  • 2, -2, 0
  • 1, -1, 0
  • \(\frac{1}{√2}\), – \(\frac{1}{√2}\)
  • None of these
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