JEE Questions for Maths Three Dimensional Geometry Quiz 6 - MCQExams.com

If direction cosines of two lines are proportional to (2, 3, -and (3, -4, 5), then the angle between them is
  • cos-1 (49/36)
  • cos-1(18√2/35)
  • 96o
  • cos-1 (18/35)
If the direction cosines of two lines are such that l + m + n = 0, l2 + m2 - n2 = 0, then the angle between then is
  • π
  • π/3
  • π/4
  • π6
The ratio in which the line joining (2, 4,, (3, 5, -is divided by the YZ-plane, is
  • 2 : 3
  • 3 : 2
  • -2 : 3
  • 4 : -3
The cosines of ∠A of the triangle with vertices A(1, -1, 2), B(6, 11,and C(1, 2,is
  • 63/65
  • 36/65
  • 16/65
  • 13/64
If P = (0, 1, 2), Q = (4, -2,and O = (0, 0, 0), then ∠POQ is equal to
  • π/6
  • π/4
  • π/3
  • π/2
If OA is equally inclined to OX, OY and OZ and if A is √3 units from the origin, then A is
  • (3, 3, 3)
  • (-1, 1, -1)
  • (-1, 1,1)
  • (1, 1, 1)
A point on X-axis which equidistant from both the points (1, 2,and (3, 5, -is
  • (-6, 0, 0)
  • (5, 0, 0)
  • (-5, 0, 0)
  • (6, 0, 0)
Let O be the origin and P be the point at a distance 3 units from origin. If direction ratios of OP are (1, -2, -2), then coordinates of P is given by
  • (1, -2, -2)
  • (3, -6, -6)
  • (1/3, -2/3, -2/3)
  • (1/9, -2/9, -2/9)
The direction cosines of the line passing through P(2, 3, -and the origin are

  • Maths-Three Dimensional Geometry-52928.png
  • 2)
    Maths-Three Dimensional Geometry-52929.png

  • Maths-Three Dimensional Geometry-52930.png

  • Maths-Three Dimensional Geometry-52931.png

Maths-Three Dimensional Geometry-52932.png

  • Maths-Three Dimensional Geometry-52933.png
  • 2)
    Maths-Three Dimensional Geometry-52934.png

  • Maths-Three Dimensional Geometry-52935.png

  • Maths-Three Dimensional Geometry-52936.png

Maths-Three Dimensional Geometry-52937.png
  • 2/9
  • 1/2
  • 9/2
  • 1/6

Maths-Three Dimensional Geometry-52939.png
  • 1
  • 2
  • 3
  • 4

Maths-Three Dimensional Geometry-52940.png
  • any value
  • excactly one value
  • exactly two values
  • exactly three values

Maths-Three Dimensional Geometry-52941.png
  • (5, 7, -2)
  • (-3, 3, 6)
  • (2, 10, 4)
  • (21, 5/3, 10/3)

Maths-Three Dimensional Geometry-52943.png

  • Maths-Three Dimensional Geometry-52944.png
  • 2)
    Maths-Three Dimensional Geometry-52945.png

  • Maths-Three Dimensional Geometry-52946.png
  • None of these

Maths-Three Dimensional Geometry-52948.png
  • Statement I is correct, Statement II is correct; Statement II is not correct explanation for Statement I
  • Statement I is correct, Statement II is incorrect
  • Statement I is correct, Statement II is correct
  • Statement I is correct, Statement Ii is correct; Statement II is correct explanation for Statement II
If lines x = 1 + s, y = -3 - λs and x = t/2 , y = 1 + t , z = 2 - t, where s and t are parameters, are coplanar, then λ is equal to
  • -1/2
  • -1
  • -2
  • 0

Maths-Three Dimensional Geometry-52950.png
  • 2√3
  • 3√3
  • 4√3
  • None of these
The direction ratios of the line x - y + z - 5 = 0 = x - 3y - 6 are
  • 3, 1, -2
  • 2, -4, 1

  • Maths-Three Dimensional Geometry-52951.png

  • Maths-Three Dimensional Geometry-52952.png

Maths-Three Dimensional Geometry-52953.png
  • 1, 5, 1/2
  • -1, 5, 1
  • -1, 5, 1/2
  • 1, 5, 1
If the line passing through the points (5, 1, a) and (3, b,crosses the YZ-plane at the point
Maths-Three Dimensional Geometry-52955.png
  • a = 8, b = 2
  • a = 2, b = 8
  • a = 4, b = 6
  • a = 6, b = 4

Maths-Three Dimensional Geometry-52957.png
  • -2
  • -5
  • 5
  • 2

Maths-Three Dimensional Geometry-52959.png

  • Maths-Three Dimensional Geometry-52960.png
  • 2)
    Maths-Three Dimensional Geometry-52961.png

  • Maths-Three Dimensional Geometry-52962.png
  • None of these
The two lines x = ay + b, z = cy + d and x = a' y + b', z = c' y + d' are perpendicular to each other, if
  • aa' + cc' = 1
  • 2)
    Maths-Three Dimensional Geometry-52963.png

  • Maths-Three Dimensional Geometry-52964.png
  • aa' + cc' = -1
The direction cosines of the line 4x - 4 = 1 - 3y = 2z - 1 are

  • Maths-Three Dimensional Geometry-52965.png
  • 2)
    Maths-Three Dimensional Geometry-52966.png

  • Maths-Three Dimensional Geometry-52967.png
  • 4, -3, 2

  • Maths-Three Dimensional Geometry-52968.png
The angle between the lines 2x = 3y = -z and 6x = -y = -4z is
  • 30o
  • 45o
  • 90o
  • 0o
If the plane x + y + z = 1 is rotated through an angle 90o about its line of intersection with the plane x - 2y + 3z = 0 then the new position of the plane is
  • x - 5y + 4z = 1
  • x - 5y + 4z = -1
  • x - 8y + 7z = 2
  • x - 8y + 7z = -2
Equation of the plane through the mid - point of the line segment joining the points P(4, 5, -, Q(-1, 2,and perpendicular to PQ is

  • Maths-Three Dimensional Geometry-52969.png
  • 2)
    Maths-Three Dimensional Geometry-52970.png

  • Maths-Three Dimensional Geometry-52971.png

  • Maths-Three Dimensional Geometry-52972.png

  • Maths-Three Dimensional Geometry-52973.png
Distance between two parallel planes 2x + y + 2z = 8 and 4x + 2y + 4z + 5 = 0 is
  • 3/2
  • 5/2
  • 7/2
  • 9/2
The equation of a plane passing through the line of intersection of the planes x + 2y + 3z = 2, x - y + z = 3 and at a distance 2/√3 from the point (3, 1, -1), is
  • 5x - 11y + z = 17
  • √2x + y = 3√2 - 1
  • x + y + z = √3
  • x - √2y = 1 - √2
0:0:1


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