CBSE  /  Class 12  /  Maths  /  Three Dimensional Geometry

  • 1. 
    The equation x² – x – 2 = 0 in three dimensional space is represented by

  • A pair of parallel planes
  • A pair of straight lines
  • A pair of perpendicular plane
  • None of these

  • 2. 
    The distance of the point (-3, 4, 5) from the origin

  • 50
  • 5√2
  • 6
  • None of these

  • 3. 
    The direction ratios of a line are 1,3,5 then its direction cosines are

  • \(\frac{1}{\sqrt{35}}\), \(\frac{3}{\sqrt{35}}\), \(\frac{5}{\sqrt{35}}\)
  • \(\frac{1}{9}\), \(\frac{1}{3}\), \(\frac{5}{9}\)
  • \(\frac{5}{\sqrt{35}}\), \(\frac{3}{\sqrt{35}}\), \(\frac{1}{\sqrt{35}}\)
  • None of these

  • 4. 
    The direction ratios of the normal to the plane 7x + 4y – 2z + 5 = 0 are

  • 7, 4,-2

  • 5. 
    The direction ratios of the line of intersection of the planes 3x + 2y – z = 5 and x – y + 2z = 3 are

  • 3, 2, -1
  • -3, 7, 5
  • 1, -1, 2
  • – 11, 4, -5

  • 6. 
    The lines of intersection of the planes \(\vec{r}\)(3\(\hat{i}\) – \(\hat{j}\) + \(\hat{k}\)) = 1 and \(\vec{r}\)(\(\hat{i}\) +4\(\hat{j}\) – 2\(\hat{k}\)) = 2 is parallel to the vector

  • 2\(\hat{i}\) + 7\(\hat{j}\) + 13\(\hat{k}\)
  • -2\(\hat{i}\) – 7\(\hat{j}\) – 13\(\hat{k}\)
  • 2\(\hat{i}\) – 7\(\hat{j}\) + 13\(\hat{i}\)

  • 7. 
    The equation of the plane through the origin and parallel to the plane 3x – 4y + 5z + 6 = 0

  • 3x – 4y – 5z – 6 = 0
  • 3x – 4y + 5z + 6 = 0
  • 3x – 4y + 5z = 0
  • 3x + 4y – 5z + 6 = 0

  • 8. 
    The locus of xy + yz = 0 is

  • A pair of st. lines
  • A pair of parallel lines
  • A pair of parallel planes
  • A pair of perpendicular planes

  • 9. 
    The plane x + y = 0

  • is parallel to z-axis
  • is perpendicular to z-axis
  • passes through z-axis
  • None of these

  • 10. 
    If α, β, γ are the angle which a half ray makes with the positive directions of the axis then sin²α + sin²β + sin²γ =

  • 1
  • 2
  • 0
  • -1
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