JEE Questions for Maths Three Dimensional Geometry Quiz 5

If a, b and c are three non - coplanar vectors, then the vector equation r = (1 - p - q) a + pb + qc represents a

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straight line
0%
plane
0%
plane passing through the origin
0%
sphere

The equation r² - 2r ∙c + h = 0, |c| > √h , represents

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circle
0%
ellipse
0%
cone
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sphere

Maths-Three Dimensional Geometry-52880.png

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0%
2)
0%
0%

The shortest distance between the straight lines through the points A₁ = (6, 2,and A₂ = (-4, 0, -in the directions of (1, -2,and (3, -2, -is

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6
0%
8
0%
12
0%
9

Maths-Three Dimensional Geometry-52885.png

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2x + 5y + z + 15 = 0
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2x - 5y - z - 15 = 0
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2x - 5y + z - 15 = 0
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2x - 5y - z + 15 = 0
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2x + 5y - z + 15 = 0

Maths-Three Dimensional Geometry-52886.png

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0
0%
2
0%
1
0%
3
0%
4

If θ is the angle between the lines AB and AC, where A, B and C are the three points with coordinates (1, 2, -1), (2, 0,and (3, -1,respectively, then √462 cos θ is equal to

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20
0%
10
0%
30
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40

A vector perpendicular to the plane containing the points A(1, -1, 2), B(2, 0, -and C(0, 2,is

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0%
2)
0%
0%

Maths-Three Dimensional Geometry-52892.png

0%
7 units
0%
13 units
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8 units
0%
9 units
0%
None of these

Maths-Three Dimensional Geometry-52893.png

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0%
2)
0%
0%
0%

The angle between the lines whose direction cosines satisfy equations l + m + n = 0 and l² = m² + n², is

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π/3
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π/4
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π/6
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π/2

The distance between the X - axis and the point (3, 12,is

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3
0%
13
0%
14
0%
12
0%
5

If the line joining A(1, 3,and B is divided by the point (-2, 3,in the ration 1 : 3, then B is equal to

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(-11, 3, 8)
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(-11, 3, -8)
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(-8, 12, 20)
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(13, 6, -13)

If the direction cosines of two lines are given by l + m + n = 0 and l² - 5m² + n² = 0, then the angle between them is

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π/2
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π/6
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π/4
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π/3

If A (3, 4, 5), B(4, 6, 3), C (-1, 2,and D(1, 0,are such that the angle between the lines DC and AB is θ, then cos θ is equal to

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7/9
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2/9
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4/9
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5/9

The direction cosines of the line joining the points (4, 3, -and (-2, 1, -are

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0%
2)
0%
0%
None of these

Find the length of the diagonal of the parallelopiped formed by planes drawn through the points (2, 3,and (5, 9,parallel to the coordinate planes.

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√38 units
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7 units
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√155 units
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13 units

If a line makes angles α, β and γ with the coordinates axes, then cos 2α + cos 2β + cos 2γ is

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-1
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-2
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2
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-3

A line AB in three dimensional space makes angles 45^o and 120^o with the positive X - axis and the positive Y - axis respectively. If AB makes an acute angle θ with the positive Z - axis, then θ equals

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30o
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45o
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60o
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75o

Let A(1, -1,and B(2, 3, -be two points. If a point P divides AB internally in the ratio 2 : 3, then the position vector of P is

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0%
2)
0%
0%
0%
None of these

If P(x, y, z) is a point on the line segment joining Q(2, 2,and R(3, 5,such that projection of OP on the axes are
Maths-Three Dimensional Geometry-52913.png

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1 : 2
0%
3 : 2
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2 : 3
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1 : 3

The distance between the points (1, 4,and (2, 2,is

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5
0%
4
0%
3
0%
2

Maths-Three Dimensional Geometry-52915.png

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0 < c < 1
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c > 2
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c = ± √2
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c = ± √3
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c = ± 3

The direction cosines of the line which is perpendicular to the lines whose direction cosines are proportional to (1, -1,and (2, 1, -are

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0%
2)
0%
0%
None of these

The XY - plane divides the line joining the points (-1, 3,and (2, -5, 6)

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internally in the ratio 2 : 3
0%
externally in the ratio 2 : 3
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internally in the ratio 3 : 2
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externally in the ratio 3 : 2

If a line in the space makes angles α, β and γ with the coordinates axes, the cos 2α + cos 2β + cos 2γ + sin² α + sin² β + sin² γ equals

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-1
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0
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1
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2

A line makes an obtuse angles with the positive X - axis and angles π/4 and π/3 with the positive Y and Z - axes respectively. Its direction cosines are