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CBSE Questions for Class 11 Engineering Maths Introduction To Three Dimensional Geometry Quiz 11 - MCQExams.com

If P(x,y,z) is a point on the line segment joining Q(2,2,4) and R(3,5,6) such that the projections of OP on the axis are 135,195,265 respectively, then P divides QR in the ratio
  • 1:2
  • 3:2
  • 2:3
  • 1:3
The points A(1,2,3);B(1,2,1);C(2,3,2) and D(4,7,6) form 
  • Square
  • Rectangle
  • Parallelogram
  • Rhombus
Find the coordinates of the points which trisect the line segment AB, given that A =( 2,1 , - 3 ) and  B =( 5 , - 8,3 ).
  • (3,2,1);(4,5,1)
  • (3,2,1);(4,5,1)
  • (3,2,1);(4,5,1)
  • (3,2,1);(4,5,1)
30 consider at three dimensional figure represented by xyz2=2, then its minimum distance from origin is 
  • 2
  • 4
  • 3
  • 1
The distances of the point P(1,2,3) from the coordinates axes are:
  • 13,10,5
  • 11,10,5
  • 13,20,15
  • 23,10,5
If O and O' are circumcenter and orthocenter of a ΔABC where ¯OA+¯OB+¯OC is λ¯OO then the value of λ is
  • 1
  • 2
  • 3
  • 4
The distance between the orthocentre and circumcentre of the triangle formed by the points (1,2,3),(3,1,5),(4,0,3) is
  • 662
  • 172
  • 552
  • 372
In the xyplane, the length of the shortest from (0,0) to (12,16) that does not go inside the circle (x6)2+(y+8)2=25 is
  • 103
  • 105
  • 103+5π3
  • 10+5π
If R divides the line segment joining P(2,3,4) and Q(4,5,6) in the ratio 3:2, then the parameter which represent R is 
  • 3
  • 2
  • 1
  • 1
Consider at three dimensional figure represented by xyz2=2, then its minimum distance from origin is
  • 2
  • 4
  • 6
  • 8
The point which is equidistant from the points (1,1,3),(2,1,2),(0,5,6) and (3,2,2) is
  • (1,3,4)
  • (3,1,4)
  • (1,3,4)
  • $$(4,1,3)$4
Minimum distance between the curves
y2=4x & x2+y212x+31=0 is -
  • 21
  • 265
  • 205
  • 215
Let A(2,3,5),B(1,3,2) and C(λ,5,μ) are the vertices of a triangle and its median through A meets side BC at D. AD is equally inclined with the axes. If E is the point on BC such that BE:EC=1:2.
Project of BA on BC
  • 2333
  • 3324
  • 2433
  • None of these
If A = (2,-3,1), B = (3,-4,6) and C is a point of trisection of AB, then Cy
  • 113
  • -11
  • 103
  • 113
The coordinates of the orthocentre of the triangle that has the coordinates of mid points of its sides as (0 , 0) (1 , 2) and ( -6 , 3) is : 
  • (0 , 0)
  • (-4 , 5)
  • (-5 , 5)
  • (-4 , 4)
Let A(2,3,5),B(1,3,2) and C(λ,5,μ) are the vertices of a triangle and its median through A meets side BC at D. AD is equally inclined with the axes. If E is the point on BC such that BE:EC=1:2.
Equation of plane containing triangle ABC
  • x+y+3=0
  • xz3=0
  • xz+3=0
  • xy+3=0
Perpendicular distance from the origin to the line joining the points (acosθ,asinθ)(acosθ,asinθ) is
  • 2acos(θϕ)
  • acos(θϕ2)
  • 4acos(θϕ2)
  • acos(θ+ϕ2)
Consider a variable plane lx+my+nz=k(k>0)andl,m,n are direction cosines of normal of the plane. Let the given plane intersects the co-ordinate axes at A,B and C, then the minimum area of ABC is _______.
  • 33k22
  • 33k24
  • 33k2
  • 123k2
The shortest distance between the point (32,0) and the curve y=x, (x>0), is:
  • 32
  • 32
  • 52
  • 54
Q, R, S are the points (2,1),(0,3)(4,0) respectively. Then the coordinates of P such that PQRS is a parallelogram is ________________.
  • (2,6)
  • (6,2)
  • (2,4)
  • (3,2)
If A=(1,2,3) and B(3,5,7) and P, Q are the points on AB such that AP=PQQB, then the mid point of PQ is?
  • (2,3,5)
  • (2,72,5)
  • (2,4,5)
  • (4,7,0)
If A=(1,2,1),B=(4,0,3);C=(1,2,1) and D=(2,4,5), then the distance between AB and CD is?
  • 23
  • 43
  • 32
  • 53
The equation of plane which is passing through the point (1,2,3) and which is at maximum distance from the point (1,0,2) is
  • 2x+2y+z=9
  • 2x+z=5
  • 3x+yz=2
  • none of these
The distance of the point (2,1,1) from the line x12=y+11=z33 measured parallel to the plane x+2y+z=4 is
  • 10
  • 20
  • 5
  • 30
A line passes through two points A(2, -3, -1) and B(8, -1, 2) the coordinates of a point on this line nearer to the origin at a distance of 14 units from A are  
  • (14 , 1, 5)
  • (-10, -7, -7)
  • (10 , 7, 7)
  • (-14, -1, -5)
If λ is the length of any edge of a regular tetrahedron, then the distance of any vertex form the opposite face is-
  • 23λ2
  • 23λ
  • 23λ
  • Noneofthese
The distance of the point (2,3) form the line x2y+5=0 measured in a direction parallel to the line x3y=0 is
  • 210
  • 10
  • 25
  • None of these
If A=(1,2,1),B=(4,0,3),C=(1,2,1),D=(2,4,5), then distance between A B and CD is
  • 13
  • 23
  • 1
  • 43
A(1,1,3), B(2,1,2) & (5,2,6) are the position vectors of the vertices of a triangle ABC. The length of the bisector of its internal angle at A is:
  • 10/4
  • 310/4
  • 10
  • None
If x-coordinates of a point P on the joining the points Q(2,2,1) and R(5,1,2) is 4, then the z-coordinates of P is
  • -2
  • -1
  • 1
  • 2
0:0:1


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