JEE Questions for Maths Three Dimensional Geometry Quiz 8 - MCQExams.com


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  • 2)
    Maths-Three Dimensional Geometry-53020.png

  • Maths-Three Dimensional Geometry-53021.png

  • Maths-Three Dimensional Geometry-53022.png
The plane 2x - 2y + z + 5 = 0 is a tangent to the sphere (x - 2)2 + (y - 2)2 + (z - 1)2 = r2, if r equals
  • 1
  • 2
  • 4
  • None of these
The centre and radius of the sphere x2 + y2 + z2 + 3x - 4z + 1 = 0 are

  • Maths-Three Dimensional Geometry-53023.png
  • 2)
    Maths-Three Dimensional Geometry-53024.png

  • Maths-Three Dimensional Geometry-53025.png

  • Maths-Three Dimensional Geometry-53026.png
The shortest distance from the plane 12x + 4y + 3z = 327 to the sphere x2 + y2 + z2 + 4x - 2y - 6z = 155 is
  • 26
  • 2)
    Maths-Three Dimensional Geometry-53027.png
  • 13
  • 39
The radius of the sphere x2 + y2 + z2 = x + 2y + 3z is
  • √14/2
  • √7
  • 7/2
  • √7/2
If (2, 3,is one end of a diameter of the sphere x2 + y2 + z2 - 6x - 12y - 2z + 20 = 0, then the coordinates of the other end of the diameter are
  • (4, 9, -3)
  • (4, -3, 3)
  • (4, 3, 5)
  • (4, 3, -3)
A plane x + y + z = -a√3 touches the sphere 2x2 + 2y2 + 2z2 - 2x + 4y - 4z + 3 = 0, then the value of a is
  • 1/√3
  • 1/2√3
  • 1 - (1/√3)
  • 1 + (1/√3)
The plane x + 2y - z = 4 cuts the sphere x2 + y2 + z2 - x + z - 2 = 0 in a circle of radius
  • √2
  • 2
  • 1
  • 3

Maths-Three Dimensional Geometry-53029.png

  • Maths-Three Dimensional Geometry-53030.png
  • (-1, -1, 0)
  • (1, 1, 1)

  • Maths-Three Dimensional Geometry-53031.png

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  • 2)
    Maths-Three Dimensional Geometry-53034.png

  • Maths-Three Dimensional Geometry-53035.png

  • Maths-Three Dimensional Geometry-53036.png

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  • (0, 6, -and (1, -2, -1)
  • (0, 6, -and (-1, -4, -2)
  • (1, -2, -and (1, 4, -2)
  • (1, -2, -and (0, -6, 1)

Maths-Three Dimensional Geometry-53038.png
  • 1/4
  • - (1/4)
  • 1/8
  • -(1/8)

Maths-Three Dimensional Geometry-53040.png
  • hyperbola
  • circle
  • straight line
  • ellipse
  • parabola

Maths-Three Dimensional Geometry-53041.png

  • Maths-Three Dimensional Geometry-53042.png
  • 2)
    Maths-Three Dimensional Geometry-53043.png

  • Maths-Three Dimensional Geometry-53044.png

  • Maths-Three Dimensional Geometry-53045.png

  • Maths-Three Dimensional Geometry-53046.png
Find the equation of the perpendicular drawn from the origin to the plane 2x + 4y - 5z = 10
  • r = (2k, 5k, 4k), k ϵ R
  • r = (2k, 4k, -5k), k ϵ R
  • r = (3k, 4k, 5k), k ϵ R
  • None of the above
The vector equation of the plane passing through the origin and the line of intersection of the plane r ∙a = λ and r ∙b = μ is
  • r ∙(λa - μb) = 0
  • r ∙(λb - μa) = 0
  • r ∙(λa + μb) = 0
  • r ∙(λb + μa) = 0

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  • Maths-Three Dimensional Geometry-53048.png
  • 2)
    Maths-Three Dimensional Geometry-53049.png

  • Maths-Three Dimensional Geometry-53050.png

  • Maths-Three Dimensional Geometry-53051.png
The vector equation of the line passing through the points (3, 2,and (-2, 1,is

  • Maths-Three Dimensional Geometry-53052.png
  • 2)
    Maths-Three Dimensional Geometry-53053.png

  • Maths-Three Dimensional Geometry-53054.png

  • Maths-Three Dimensional Geometry-53055.png

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  • 10/9
  • 3/10
  • 10/3√3
  • 10/9

Maths-Three Dimensional Geometry-53057.png
  • (3, 1, 4)
  • (1, 3, 4)
  • (1, 2, 4)
  • None of these
Though the point P(α, β, γ), a plane is drawn at right angle to OP to meet the coordinate axes at A, B, C respectively. IF OP = p, then equation of the plane ABC is
  • αx + βy + γz = p
  • 2)
    Maths-Three Dimensional Geometry-53058.png
  • 2αx + 2βy + 2γz = p2
  • αx + βy + γz = p2

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  • Maths-Three Dimensional Geometry-53060.png
  • 2)
    Maths-Three Dimensional Geometry-53061.png

  • Maths-Three Dimensional Geometry-53062.png

  • Maths-Three Dimensional Geometry-53063.png

  • Maths-Three Dimensional Geometry-53064.png
The equation of the plane passing through three non - collinear points a, b, c is
  • r∙(b × c + c × a + a × b) = 0
  • r∙(b × c + c × a + a × b) = [a b c]
  • r∙[ a ×(b × c)] = [a b c]
  • r∙(a + b + c) = 0
The vector equation of the sphere whose centre is the point (1, 0,and radius is 4, is

  • Maths-Three Dimensional Geometry-53065.png
  • 2)
    Maths-Three Dimensional Geometry-53066.png

  • Maths-Three Dimensional Geometry-53067.png

  • Maths-Three Dimensional Geometry-53068.png

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  • Maths-Three Dimensional Geometry-53070.png
  • 2)
    Maths-Three Dimensional Geometry-53071.png

  • Maths-Three Dimensional Geometry-53072.png

  • Maths-Three Dimensional Geometry-53073.png
If the points (–1, 2, – 3), (4, a,and (b, 8,are collinear, then a and b are respectively equal to
  • 5 and 5
  • 9 and 5
  • 5 and 9
  • –5 and 9
The triangle formed by the points (0, 7,10), (–1, 6, 6), (–4, 9,is
  • Equilateral
  • Isosceles
  • Right-angled
  • Right-angled isosceles

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  • Maths-Three Dimensional Geometry-53077.png
  • 2)
    Maths-Three Dimensional Geometry-53078.png

  • Maths-Three Dimensional Geometry-53079.png

  • Maths-Three Dimensional Geometry-53080.png

Maths-Three Dimensional Geometry-53082.png
  • 20
  • 10
  • 30
  • 40
The direction cosines of a line equally inclined to all the three rectangular co-ordinate axis are

  • Maths-Three Dimensional Geometry-53084.png
  • 2)
    Maths-Three Dimensional Geometry-53085.png
  • 1, 1, 1
  • None of these
0:0:1


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