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JEE Questions for Maths Three Dimensional Geometry Quiz 3 - MCQExams.com
JEE
Maths
Three Dimensional Geometry
Quiz 3
If foot of the perpendicular from B(-2, 1,to plane is (3, 1, 2). Then, the equation of the plane is
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4x - 2y = 11
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5x - 2y = 10
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5x - 2z = 11
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5x + 2z = 11
If θ is the angle between the planes 2
x
- y + z - 1 = 0 and
x
- 2y + z + 2 = 0, then cos θ is equal to
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2/3
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3/4
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4/5
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5/6
The plane 2λ
x
- (1 + λ)y + 3z = 0 passes through the intersection of the planes
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2x - y = 0 and y + 3z = 0
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2x - y = 0 and y - 3z = 0
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2x + 3z = 0 and y = 0
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None of the above
The reflection of the plane 2
x
- 3y + 4z - 3 = 0 in the plane
x
- y + z - 3 = 0 is the plane
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4x - 3y + 2z - 15 = 0
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x - 3y + 2z - 15 = 0
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4x + 3y - 2z + 15 = 0
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None of these
The equation of plane passing through a point A(2, -1,and parallel to the vectors a = (3, 0, -and b = (-3, 2,is
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2x - 3y + 6z - 25 = 0
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2x - 3y + 6z + 25 = 0
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3x - 2y + 6z - 25 = 0
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3x - 2y + 6z + 25 = 0
The points A(4, 5, 1), B(0, -1, -1), C(3, 9,and D(-4, 4,are
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collinear
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coplanar
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non - coplanar
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non - collinear
The equation of the plane which the axes in A, B, C such that the centroid of ∆ABC is
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x + y + z = 1
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x + y + z = 2
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x + y + z = 1/3
If O is the origin and A is the point (a, b, c), then the equation of the plane through A and right angles to OA is
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a(x - a) - b(y - b) - c(z - c) = 0
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a(x + a) + b(y + b) + c(z + c) = 0
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a(x - a) + b(y - b) + c(z - c) = 0
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None of the above
The image of the point (5, 4,in the plane
x
+ y + 2z - 15 = 0 is
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(3, 2, 2)
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(2, 3, 2)
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(2, 2, 3)
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(-5, -4, -6)
The equation of the plane through the point (1, 2,and parallel to the plane
x
+ 2y + 5z = 0 is
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(x -+ 2(y -+ 5(z -= 0
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x + 2y + 5z = 14
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x + 2y + 5z = 16
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None of the above
The equation of the plane passing through the points (0, 1, 2), (-1, 0,and perpendicular to the plane 2
x
+ 3y + z = 5 is
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3x - 4y + 18z + 32 = 0
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3x + 4y - 18x + 32 = 0
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4x + 3y - 17z + 31 = 0
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4x - 3y + z + 1 = 0
The distance of the point (1, -5,from the plane
x
- y + z = 5 measured along a straight
x
= y = z is 2√3k, then the value of k is
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5
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6
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√3
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4
The line joining points (1, 1,and (3, -2,meets the plane 3
x
+ 2y + z = 6 at the point
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(1, 1, 2)
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(3, -2, 1)
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(2, -3, 1)
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(3, 2, 1)
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2x + 3y + z = 17
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x + 2y + 3z = 9
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3x + 2y + z = 16
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x + 2y + 3z = 20
Equation of the line through the point (2, 3,and parallel to the line of intersection of the planes
x
- 2y - z + 5 = 0 and
x
+ y + 3z = 6 is
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2)
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0%
0%
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3x + 4y + 5z = 7
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2x + 3y + 4z = 0
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x + y - z = 2
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2x + y - 2z = 0
The point P is the intersection of the straight line joining the points Q(2, 3,and R(1, -1,with the plane 5
x
- 4y - z = 1. If S is the foot of the perpendicular drawn from the point T(2, 1,to QR, then the length of the line segment PS is
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1/√2
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√2
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2
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2√2
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y + 2z = -1
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y + z = -1
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y - z = 1
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y - 2z = -1
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0%
2)
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0%
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x + 2y - 2z = 0
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3x + 2y - 2z = 0
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x - 2y + z = 0
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5x + 2y - 4z = 0
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1/2
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3/2
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3
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4
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5/2
If Q is the image of the point P(2, 3,under the reflection in the plane
x
- 2y + 5z = 6, then the equation of the line PQ is
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2)
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0%
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13
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12
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11
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8
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7
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x + y + z = 1
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x + y + z = 2
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x + y + z = 0
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None of these
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√120
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√83
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2√19
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√78
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x - y + z = 1
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x + y + z = 5
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x + 2y - z = 0
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2x - y + z = 5
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Statement I is correct, Statement II is correct; Statement II is correct explanation for Statement I
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Statement I is correct, Statement II is correct; Statement II is not a correct explanation for Statement II
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Statement I is correct, Statement II is incorrect
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Statement I is incorrect, Statement II is correct
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- (4/3)
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3/4
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-3/5
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5/3
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x + 5y - 3z = 0
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x - 5y + 3z = 0
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x - 5y + 3z = 0
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3x - 10y + 5z = 0
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x + 5y + 3z = 0
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4
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-4
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2
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-2
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0
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