JEE Questions for Maths Three Dimensional Geometry Quiz 1

The distance of a point P(a, b, c) from the X - axis is

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0%
2)
0%
a
0%

The angle between two diagonals of a cube is

0%
cos-1 (1/3)
0%
30o
0%
cos-1 (1/√3)
0%
45o

Maths-Three Dimensional Geometry-52701.png

0%
0%
2)
0%
0%

The angle between a normal to the plane 2x - y + 2z - 1 = 0 and the Z - axis is

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cos-1 (1/3)
0%
sin-1 (2/3)
0%
cos-1 (2/3)
0%
sin-1 (1/3)
0%
sin-1 (3/5)

The angle between the lines, whose direction ratios are (1, 1,, (√3, -1, -√3 - 1, 4), is

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cos-1 (1/65)
0%
π/6
0%
π/3
0%
π/2

The projection of any line on coordinate to the respectively 3, 4 and 5, then its length is

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50
0%
12
0%
5√2
0%
None of these

A line makes the same angle θ with each of the X and Z - axes. If it makes the angle β with Y - axis such that sin² β = 3 sin²θ, then cos² θ equals

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3/5
0%
1/5
0%
2/5
0%
2/3

The shortest distance of the point (1, 2,from X, Y and Z - axes respectively are

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1, 2, 3
0%
2)
0%
0%

The projection of a directed line segment on the coordinate axes are 12, 4,3. The direction cosines of the line are

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0%
2)
0%
0%

If (1, -2, -and (0, 2,are direction ratios of two lines, then the direction cosines of a perpendicular to both the lines are

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0%
2)
0%
0%

The ratio in which ZX - plane divides the line segment AB joining the points A(4, 2,and B(-2, 4,is equal to

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1 : 2 internally
0%
1 : 2 externally
0%
-2 : 1
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None of these

The vectors of magnitude a, 2a, 3a meet at a point and their directions are along the diagonals of three adjacent faces of a cube. Then, the magnitude of their resultant is

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5a
0%
6a
0%
10a
0%
9a

A point on XOZ-plane divides the join of (5, -3, -and (1, 2, -at

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0%
2)
0%
(5, 0, 2)
0%
(5, 0, -2)

The perimeter of the triangle with vertices at (1, 0, 0), (0, 1,and (0, 0,is

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3
0%
2
0%
2√2
0%
3√2

In ∆ABC, the mid - points of the sides AB, BC and CA are respectively (1, 0, 0), (0, m, and (0, 0, n). Then,
Maths-Three Dimensional Geometry-52725.png

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2
0%
4
0%
8
0%
16

If a line makes angles α, β, γ and δ with four diagonals of a cube, then the value of sin² α + sin² β + sin² γ + sin²

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4/3
0%
8/3
0%
7/3
0%
1

The angle between the lines whose direction cosines are
Maths-Three Dimensional Geometry-52726.png

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π
0%
π/2
0%
π/3
0%
π/4

If a line makes an angle of π/4 with the positive directions of each of X and Y - axes, then the angle that the line makes with the positive to the Z-axis is

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π/6
0%
π/3
0%
π/4
0%
π/2

The perpendicular distance of the point (6, 5,from Y-axis is

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5 units
0%
6 units
0%
8 units
0%
9 units
0%
10 units

What are the DR's of vector parallel to (2, -1,and (3, 4, -?

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(1, 5, -2)
0%
(-2, -5, 2)
0%
(-1, 5, 2)
0%
(-1, -5, -2 )

Maths-Three Dimensional Geometry-52728.png

0%
3
0%
π - 3
0%
4
0%
π - 4

Maths-Three Dimensional Geometry-52729.png

0%
0%
2)
0%
0%

Maths-Three Dimensional Geometry-52734.png

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k = 2
0%
k = 0
0%
k = 3
0%
k = -1

Maths-Three Dimensional Geometry-52736.png

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0%
2)
0%
0%
0%
0

The angle between the lines x = 1, y = 2 and y = -1, z = 0 is

0%
30o
0%
60o
0%
90o
0%
0o

Maths-Three Dimensional Geometry-52741.png

0%
-10/7
0%
10/7
0%
-10/11
0%
10/11
0%
10/9

The distance of the point P(1, 2,from the line which passes through the point A(4, 2,and parallel to the vector
Maths-Three Dimensional Geometry-52742.png