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JEE Advanced Level Test: Three Dimensional 3D Geometry- 1 - Question 1

A line makes angles α,β,γ with the coordinates axes. If α+β = 90°, then (gamma) equal to

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JEE Advanced Level Test: Three Dimensional 3D Geometry- 1 - Question 2

The coordinates of the point A, B, C, D are (4, α, 2), (5, –3, 2), (β, 1, 1) & (3, 3, – 1). Line AB would be perpendicular to line CD when

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JEE Advanced Level Test: Three Dimensional 3D Geometry- 1 - Question 3

The locus represented by xy + yz = 0 is

JEE Advanced Level Test: Three Dimensional 3D Geometry- 1 - Question 4

The equation of plane which passes through (2, –3, 1) & is normal to the line joining the points (3, 4, –1) & (2, – 1, 5) is given by

Detailed Solution for JEE Advanced Level Test: Three Dimensional 3D Geometry- 1 - Question 4

JEE Advanced Level Test: Three Dimensional 3D Geometry- 1 - Question 5

If the sum of the squares of the distances of a point from the three coordinate axes be 36, then its distance from the origin is

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JEE Advanced Level Test: Three Dimensional 3D Geometry- 1 - Question 6

The locus of a point P which moves such that PA^{2} – PB^{2} = 2k^{2} where A and B are (3, 4, 5) and (–1, 3, –7) respectively is

JEE Advanced Level Test: Three Dimensional 3D Geometry- 1 - Question 7

The equation of the plane passing through the point (1, – 3, –2) and perpendicular to planes x + 2y + 2z = 5 and 3x + 3y + 2z = 8, is

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JEE Advanced Level Test: Three Dimensional 3D Geometry- 1 - Question 8

A variable plane passes through a fixed point (1, 2, 3). The locus of the foot of the perpendicular drawn from origin to this plane is

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JEE Advanced Level Test: Three Dimensional 3D Geometry- 1 - Question 9

The reflection of the point (2, –1, 3) in the plane 3x – 2y – z = 9 is

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JEE Advanced Level Test: Three Dimensional 3D Geometry- 1 - Question 10

The distance of the point (–1, –5, –10) from the point of intersection of the line, and the plane, x – y + z = 5, is

JEE Advanced Level Test: Three Dimensional 3D Geometry- 1 - Question 11

The distance of the point (1, –2, 3) from the plane x – y + z = 5 measured parallel to the line,

JEE Advanced Level Test: Three Dimensional 3D Geometry- 1 - Question 12

The straight l ines and

JEE Advanced Level Test: Three Dimensional 3D Geometry- 1 - Question 13

If plane cuts off intercepts OA = a, OB = b, OC = c from the coordinate axes, then the area of the triangle ABC equal to

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JEE Advanced Level Test: Three Dimensional 3D Geometry- 1 - Question 14

A point moves so that the sum of the squares of its distances from the six faces of a cube given by x = ± 1, y = ± 1, z = ± 1 is 10 units. The locus of the point is

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JEE Advanced Level Test: Three Dimensional 3D Geometry- 1 - Question 15

A variable plane passes through a fixed point (a, b, c) and meets the coordinate axes in A, B, C. Locus of the point common to the planes through A, B, C and parallel to coordinate plane, is

Detailed Solution for JEE Advanced Level Test: Three Dimensional 3D Geometry- 1 - Question 15

JEE Advanced Level Test: Three Dimensional 3D Geometry- 1 - Question 16

Two systems of rectangular axes have same origin. If a plane cuts them at distances a, b, c and a_{1}, b_{1}, c_{1 }from the origin, then

JEE Advanced Level Test: Three Dimensional 3D Geometry- 1 - Question 17

The angle between the plane 2x – y + z = 6 and a plane perpendicular to the planes x + y + 2z = 7 and x – y = 3 is

JEE Advanced Level Test: Three Dimensional 3D Geometry- 1 - Question 18

The non zero value of ‘a’ for which the lines 2x – y + 3z + 4 = 0 = ax + y – z + 2 and x – 3y + z = 0 = x + 2y + z + 1 are co-planar is

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JEE Advanced Level Test: Three Dimensional 3D Geometry- 1 - Question 19

If the lines and are concurrent then

Detailed Solution for JEE Advanced Level Test: Three Dimensional 3D Geometry- 1 - Question 19

JEE Advanced Level Test: Three Dimensional 3D Geometry- 1 - Question 20

The coplanar points A, B, C, D are (2 – x, 2, 2), (2, 2 – y, 2), (2, 2, 2 – z) and (1, 1, 1) respectively. Then

Detailed Solution for JEE Advanced Level Test: Three Dimensional 3D Geometry- 1 - Question 20

JEE Advanced Level Test: Three Dimensional 3D Geometry- 1 - Question 21

The direction ratios of a normal to the plane through (1, 0, 0), (0, 1, 0), which makes an angle of π/4 with the plane x + y = 3 are

JEE Advanced Level Test: Three Dimensional 3D Geometry- 1 - Question 22

Let the points A(a, b, c) and B(a^{'}, b^{'}, c^{'}) be at distances r and r^{'} from origin. The line AB passes through origin when

JEE Advanced Level Test: Three Dimensional 3D Geometry- 1 - Question 23

Let L be the line of intersection of the planes 2x + 3y + z = 1 and x + 3y + 2z = 2. If L makes an angle ? with the positive x-axis, the cos α equals

JEE Advanced Level Test: Three Dimensional 3D Geometry- 1 - Question 24

If a line makes an angle of π/4 with the positive directions of each of x-axis and y-axis, then the angle that the line makes with the positive direction of the z-axis is

JEE Advanced Level Test: Three Dimensional 3D Geometry- 1 - Question 25

If the angle θ between the line and the plane is such that sinθ = 1/3 The value of λ is

JEE Advanced Level Test: Three Dimensional 3D Geometry- 1 - Question 26

A line makes the same angle θ with each of the x and z-axis. If the angle θ, which it makes with y-axis is such that sin^{2} β = 3 sin^{2} θ, then cos^{2}θ equals

JEE Advanced Level Test: Three Dimensional 3D Geometry- 1 - Question 27

Distance between two parallel planes 2x + y + 2z = 8 and 4x + 2y + 4z + 5 = 0 is

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JEE Advanced Level Test: Three Dimensional 3D Geometry- 1 - Question 28

A line with direction cosines proportional to 2, 1, 2 meets each of the lines x = y + a = z and x + a = 2y = 2z. The co-ordinates of each of the points of intersection are given by

Detailed Solution for JEE Advanced Level Test: Three Dimensional 3D Geometry- 1 - Question 28

JEE Advanced Level Test: Three Dimensional 3D Geometry- 1 - Question 29

The lines and are coplanar if

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JEE Advanced Level Test: Three Dimensional 3D Geometry- 1 - Question 30

The equation of plane which meet the co-ordinate axes whose centroid is (a, b, c)

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