12th Standard cbse -- Maths - Three Dimensional Geometry

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Question - 1

The distance of point (2, 5, 7) from the x-axis is

  • A 2
  • B \(\sqrt{74}\)
  • C \(\sqrt{29}\)
  • D \(\sqrt{53}\)

Question - 2

P is a point on the line segment joining the points (3, 5, -1) and (6, 3, -2). If y-coordinate of point P is 2, then its x-coordinate will be

  • A 2
  • B \(\frac{17}{3}\)
  • C \(\frac{15}{3}\)
  • D -5

Question - 3

Direction ratios of a line are 2, 3, -6. Then direction cosines of a line making obtuse angle with the y-axis are

  • A \(\frac { 2 }{ 7 } ,\frac { -3 }{ 7 } ,\frac { -6 }{ 7 } \)
  • B \(\frac { -2 }{ 7 } ,\frac { 3 }{ 7 } ,\frac { -6 }{ 7 } \)
  • C \(\frac { -2 }{ 7 } ,\frac { -3 }{ 7 } ,\frac { 6 }{ 7 } \)
  • D \(\frac { -2 }{ 7 } ,\frac { -3 }{ 7 } ,\frac { -6 }{ 7 } \)

Question - 4

A line makes angle α, β, γ with x-axis, y-axis and z-axis respectively then cos 2α + cos 2β + cos 2γ is equal to

  • A 2
  • B 1
  • C -2
  • D -1

Question - 5

The equations of y-axis in space are

  • A x = 0, y = 0
  • B x = 0, z = 0
  • C y = 0, z = 0
  • D y = 0

Question - 6

 

If the direction cosines of a line are  \(\frac{k}{3}\)\(\frac{k}{3}\)\(\frac{k}{3}\) then value of k is

  • A k > 0
  • B  0 < k < 1.
  • C   k = \(\frac13\)
  • D k = ± 73

Question - 7

Distance of plane \(\overrightarrow { r } .(2\widehat { i } +3\widehat { j } -6\widehat { k } )+2=0\) from origin is

  • A 2
  • B 14
  • C \(\frac27\)
  • D -\(\frac27\)

Question - 8

Distance between planes \(\overrightarrow { r } .(2\widehat { i } +\widehat { j } -2\widehat { k } )+5=0\) and \(\overrightarrow { r } .(6\widehat { i } +3\widehat { j } -6\widehat { k } )+2=0\) is

  • A \(\frac { 9 }{ 13 } \)
  • B \(\frac { 15 }{ 4 } \)
  • C \(\frac { 13 }{ 9 } \)
  • D \(\frac { 1 }{ 13 } \)

Question - 9

Distance between the two planes: 2x + 3y + 4z = 4 and 4x + 6y + 8z = 12 is

  • A 2 units
  • B 4 units
  • C 8 units
  • D \(\frac{2}{\sqrt{29}}\)

Question - 10

The planes: 2x – y + 4z = 5 and 5x – 2.5y + 10z = 6 are

  • A Perpendicular
  • B Parallel
  • C intersect y-axis
  • D passes through \((0,0,\frac{5}{4})\)