JEE Questions for Maths Three Dimensional Geometry Quiz 9

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2
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1
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3
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0

Maths-Three Dimensional Geometry-53089.png

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2)
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None of these

All the points on the x-axis have

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x = 0
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y = 0
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x = 0, y = 0
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y = 0, z = 0

If a line lies in the octant OXYZ and it makes equal angles with the axis, then

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2)
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The pairs of rectangular co-ordinate planes have equations

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xy = yz = 0
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x = y = z = 0
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xyz = 0
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None of these

The points A(1, 0, 1), B(–1, 2,and C(0, 1,are

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Non-collinear
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Collinear
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Non-coplanar
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None of the above

If the centroid of triangle whose vertices are (a, 1, 3), (–2, b, –and (4, 7, c) be the origin, then the values of a, b, c are

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–2, – 8, – 2
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2, 8, – 2
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–2, – 8, 2
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7, – 1, 0

Which of the following set of points are non-collinear

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(1, – 1, 1), (–1, 1, 1), (0, 0, 1)
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(1, 2, 3), (3, 2, 1), (2, 2, 2)
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(–2, 4, – 3), (4, – 3, – 2), (–3, – 2, 4)
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(2, 0,– 1), (3, 2, – 2), (5, 6, – 4)

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

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None of these

If a line makes angles of 30° and 45° with x-axis and y-axis, then the angle made by it with z-axis is

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45°
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60°
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120°
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None of these

Direction ratios of the normal to the plane passing through the points (0, 1, 1), (1, 1,and (–1, 2, –are

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(1, 1, 1)
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(2, 1,–1)
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(1, 2, –1)
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(1,–2,–1)

If the length of a vector be 21 and direction ratios be 2, – 3, 6 then its direction cosines are

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None of these

If the co-ordinates of the points P, Q, R, S be (1, 2, 3), (4, 5, 7), (–4, 3, –and (2, 0,respectively, then

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PQ = RS
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None of these

The shortest distances of the point (1, 2,from the axis x, y and z respectively are

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1, 2, 3
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2)
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If the co-ordinates of the points P and Q be (1, – 2,and (2, 3,and O be the origin, then

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None of these

The number of straight lines that are equally inclined to the three dimensional co-ordinate axis, is

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2
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4
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6
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8

If θ is the angle between the lines AB and CD, then projection of line segment AB on line CD, is

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AB sin θ
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AB cos θ
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AB tan θ
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CD cos θ

If A(1, 2, –and B(–1, 0,are given, then the co-ordinates of P which divides AB externally in the ratio 1: 2 are

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None of these

The point of intersection of the line joining the points (3, 4,and (5, 1,and the xy–plane is

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2)
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If the co-ordinates of A and B be (1, 2,and (7, 8, 7), then the projections of the line segment AB on the co-ordinate axis are

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6, 6, 4
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4, 6, 4
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3, 3, 2
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2, 3, 2

The co-ordinates of the point P are (x, y, z) and the direction cosines of the line OP when O is the origin, are l, m, n. If OP = r, then

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l = x, m = y, n = z
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l = xr, m = yr, n = zr
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x = lr, y = mr, z = nr
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None of these

A line makes angles α, β, γ with the co-ordinate axis. If α + β = 90°, then γ =

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0
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90°
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180°
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None of these

Points (–2, 4, 7), (3, – 6, –and (1, – 2, –are

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Collinear
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Vertices of an equilateral triangle
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Vertices of an isosceles triangle
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None of the above

Maths-Three Dimensional Geometry-53136.png

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1
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A line AB in three-dimensional space makes angle 45° and 120° with the positive x-axis and the positive y-axis respectively. If AB makes an acute angle θ with the positive respectively. If AB makes an acute angle θ with the positive z-axis, then θ equals