JEE Questions for Maths Three Dimensional Geometry Quiz 2

The foot of the perpendicular from (2, 4, -to the line x + 5 = 1/4 (y += 1/9 (z -is

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(-4, 1, -3)
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(4, -1, -3)
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(-4, -1, 3)
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(-4, -1, -3)

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

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(3a, 3a, 3a), (a, a, a)
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(3a, 2a, 3a), (a, a, a)
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(3a, 2a, 3a), (a, a, 2a)
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(2a, 3a, 3a), (2a, a, a)

The equation of the straight line passing through the points (4, -5, -and (-1, 5, 3)

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2)
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0%

Maths-Three Dimensional Geometry-52757.png

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3
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√11
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√13
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5

Maths-Three Dimensional Geometry-52758.png

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(0, 0, 0)
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(1, 1, 1)
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(-1, -1, -1)
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(1, 2, 3)

If the points (1, 2,and (2, -1,lie on the opposite sides of the plane 2x + 3y - 2z = k, then

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k < 1
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k > 2
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k < 1 or k > 2
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1 < k < 2

The volume of the tetrahedron included between the plane 3x + 4y - 5z - 60 = 0 are coordinate plane is

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60
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600
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720
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400

If a plane meets the coordinate axes at A, B and C such that the centroid of the triangle is (1, 2, 4), then the equation of the plane is

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x + 2y + 4z = 12
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4x + 2y + z = 12
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x + 2y + 4z = 3
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4x + 2y + z = 3

The equation of the plane through the intersection of the plane 3x - y + 2z - 4 = 0, x + y + z - 2 = 0 and the point (2, 2,is

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7x - 5y + 4z - 8 = 0
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None of these
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7x + 5y + 4z + 8 = 0
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7x + 5y + 4z - 8 = 0

Maths-Three Dimensional Geometry-52762.png

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0%
2)
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0%

Foot of the perpendicular drawn from the origin to the plane 2x - 3y + 4z = 29 is

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(5, -1, 4)
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(7, -1, 3)
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(5, -2, 3)
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(2, -3, 4)
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(1, -3, 4)

The equation of the plane passing through the points (2, 2, 1), (9, 3,and perpendicular to the plane 2x + 6y + 6z = 1 is

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2x - 4y + 5z - 9 = 0
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3x + 4y - z - 5 = 0
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3x + 4y - 5z - 9 = 0
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x + 4y - 9z - 3 = 0

A equation of a plane parallel to the plane x - 2y + 2z - 5 = 0 and at a unit distance from the origin is

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x - 2y + 2z ± 3 = 0
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x - 2y + 2z + 1 = 0
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x - 2y + 2z - 1 = 0
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x - 2y + 2z + 5 = 0

The image of the point (1, 3,with respect to the plane 2x - y + z = 0 is

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(-1, 4, 3)
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(-3, 5, 2)
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(1, 3, 4)
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(-1, -3, -4)

An equation of the plane through the points (1, 0, 0), (0, 2,and at a distance 6/7 units from the origin, is

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6x + 3y + z - 6 = 0
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6x + 3y + 2z - 6 = 0
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6x + 3y + z + 6 = 0
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6x + 3y + 2z + 6 = 0
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6x + 2y + 3z + 6 = 0

The equation of the plane that contains the point (1, -1,and is perpendicular to each of the planes 2x + 3y - 2z = 5 and x + 2y - 3z = 8 is

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5x + 4y - z = 7
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5x - 4y + z = 7
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-5x + 4y - z = 7
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5x - 4y - z = 7

The equation of the plane perpendicular to Z - axis and passing through (2, -3,is

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x - 2 = 0
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y + 3 = 0
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z - 5 = 0
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2x - 3y + 5z + 4 = 0

Equation of the plane passing through the intersection of the planes x + y + z = 6, 2x + 3y + 4z + 5 = 0 and the point (1, 1,is

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20x + 23y + 26z - 69 = 0
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31x + 45y + 49z + 52 = 0
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8x + 5y + 2z - 69 = 0
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4x + 5y + 6z - 7 = 0

A plane makes intercepts a, b, c at A, B, C on the coordinates axes, respectively. If the centroid of ∆ABC is at (3, 2, 1), then the equation of the plane is

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x + 2y + 3z = 9
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2x - 3y - 6z = 18
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2x + 3y + 6z = 18
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2x + y + 6z = 18
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2x + 3y + 6z = 9

If a plane passes through the point P(-1, -1,and also passes through a line joining the points Q(0, 1,and R(0, 0, 2). Then, the distance of plane from the point (0, 0,is

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3
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0
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1/√6
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2/√6

If the line drawn from (4, -1,to the point (-3, 2,meets a plane at right angle at the point (-10, 5, 4), then the equation of plane is

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7x + 3y + z + 89 = 0
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7x - 3y - z + 89 = 0
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7x - 3y + z + 89 = 0
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None of these

The equation of the plane passing through the line of intersection of the planes x + y + z = 6, 2x + 3y + 4z + 5 = 0 and perpendicular to the plane 4x + 5y - 3z = 8 is

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x + 7y + 13z - 96 = 0
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x + 7y + 13z + 96 = 0
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x + 7y - 13z - 96 = 0
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x - 7y + 13z + 96 = 0

Let P(-7, 1, -be a point on a plane and O be the origin. If OP is normal to the plane, then the equation of the plane is

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7x - y + 5z + 75 = 0
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7x + y - 5z + 73 = 0
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7x + y + 5z + 73 = 0
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7x - y - 5z + 75 = 0
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7x - y - 5z + 73 = 0

The equation to the plane passing through the points (2, 3,and (4, -5,parallel to X - axis is

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x + y + 4z = 7
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x + 4z = 7
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y - 4z = 7
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y + 4z = -7
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y + 4z = 7

If a plane meets the coordinate axes at A, B and C in such a way that the centroid of ∆ABC is at the point (1, 2, 3), then the equation of the plane is

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2)
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None of these

If the foot of the perpendicular from (0, 0,to plane is (1, 2, 2), then the equation of the plane is

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-x + 2y + 8z - 9 = 0
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x + 2y + 2z - 9 = 0
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x + y + z - 5 = 0
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x + 2y - 3z + 1 = 0

The equation of the plane passing through the points (a, 0, 0), (0, b,and (0, 0, c) is

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ax + by + cz = 0
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ax + by + cz = 1
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0%

The equation of the plane passing through the mid - point of the line of joining of the points (1, 2, 3), (3, 4,and perpendicular to it is

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x + y + z = 9
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x + y + z = -9
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2x + 3y + 4z = 9
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2x + 3y + 4z = -9

If a plane passes through (1, -2,and is perpendicular to two planes 2x - 2y + z = 0 and x - y + 2z = 4, then the distance of the plane from the point (1, 2,is

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0
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1
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√2
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2√2

If a variable plane moves, so that sum of the reciprocals of its intercepts on the coordinate axes is 1/2 Then, the plane passes through

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(1, 1, 1)
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(2, 2, 2)
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(0, 0, 0)

JEE Questions for Maths Three Dimensional Geometry Quiz 2 - MCQExams.com

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Practice Maths Quiz Questions and Answers

JEE Questions for Maths Three Dimensional Geometry Quiz 2 - MCQExams.com

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Practice Maths Quiz Questions and Answers

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