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CBSE Questions for Class 11 Engineering Maths Introduction To Three Dimensional Geometry Quiz 10 - MCQExams.com

The distance of P(2,-3) from the x-axis is......
  • 2
  • -3
  • 3
  • 13
If the distance between the points (2,-3) and (5,b) is 5 , then b=.........
  • 1
  • 2
  • 7
  • 5
Find the centroid of a triangle, mid-points of whose sides are (!,2,3),(3,0,1) and (1,1,4)
  • (1,1,2)
  • (1,2,2)
  • (1,1,2)
  • (1,1,2)
The point in the xy plane which is equidistant from (2,0,3),(0,3,2) and (0,0,1) is 
  • (1,2,3)
  • (3,2,0)
  • (3,2.0)
  • (3,2,0)
  • (3,2,1)
The foot of the perpendicular from the point A(7,14,5) to the plane 2x+4yz=2 is?
  • (3,1,8)
  • (1,2,8)
  • (3,3,5)
  • (5,3,4)
The coordinates of the point where the line through the points A(5,1,6) and B(3,4,1) crosses the yz-plane is
  • (0,17,13)
  • (0,172,132)
  • (0,172,132)
  • none of these
The point on the line x21=y+32=z+52 at a distance of 6 from the point (2,3,5) is
  • (3,5,3)
  • (4,7,9)
  • (0,2,1)
  • (3,5,3)
The distance between two points P and Q is d and the length of their projections of PQ on the coordinate planes are d1,d2,d3. Then d21+d22+d23=kd2 where K is
  • 1
  • 5
  • 3
  • 2
The shortest distance between the lines x32=y+157=z95 and x+12=y11=z93 is
  • 23
  • 43
  • 36
  • 56
The ratio in which the plane r(i2j+3k)=17 divides the line joining the points 2i+4j+7k and  3i5j+8k
  • 1 : 5
  • 1 : 10
  • 3 : 5
  • 3 : 10
The point on the line x21=y+32=z+52 at a distance of 6 from the point (2,3,5) is
  • (3,5,3)
  • (4,7,9)
  • (0,2,1)
  • (3,5,3)
The points A(1,2,1),B(2,5,2),C(4,4,3) and D(3,1,2) are
  • collinear
  • vertices of a rectangle
  • vertices of a square
  • vertices of a rhombus
Let A(2ˆi+3ˆj+5ˆk)B(ˆi+3ˆj+2ˆk)and C(λˆi+5ˆj+μˆk) are vertices of a triangle and its median through A is equally inclined to the positive directions of the axes. The value of λ+μ is equal to
  • 7
  • 2
  • 7
  • 17
If (0,b,0) is the centroid of the triangle formed by the points (4,2,3) , (a,5,1) and (2,6,2) . If a,b are the roots of the quadratic equation x2+px+q=0, then p,q are 
  • 9,18
  • 9,18
  • 3,18
  • 3,18
lf OABC is a tetrahedron such that the OA2+BC2=OB2+CA2=OC2+AB2, then which of the following is/are correct
  • ABOC
  • OBCA
  • OC=AB
  • ABBC
The plane ax+by+cz+(3)=0 meet the co-ordinate axes in A,B,C. The centroid of the triangle is
  • (3a,3b,3c)
  • (3a.3b,3c)
  • (a3.b3,c3)
  • (1a.1b,1c)
ABCD is a parallelogram. L is a point on BC  which divides BC in the ratio 1:2. AL intersects BD at P. M is a point on DC which divides DC in the ratio 1:2 and AM intersects BD in Q.

Point P divides AL in the ratio
  • 1:2
  • 1:3
  • 3:1
  • 2:1
If the vertices of a triangle are (1,6,4),(2,1,1) and (5,1,0) then the centroid of the triangle is
  • (6,6,3)
  • (2,2,1)
  • (3,3,32)
  • none of these
The coordinates of a point which is equidistant from the point (0,0,0),(a,0,0),(0,b,0) and (0,0,c) are given by
  • (a2,b2,c2)
  • (a2,b2,c2)
  • (a2,b2,c2)
  • (a2,b2,c2)
If A=(0,0,2),B=(2,2,2),C=(2,2,0) and D=(822017,122+417,208217), then ABCD is a
  • rhombus
  • square
  • parallelogram
  • none of these
The equation of motion of a rocket are: x=2t,y=4t,z=4t, where the time t is given in seconds and the coordinate of a moving point in kilometers. At what distance will the rocket be from the starting point O(0,0,0) in 10 seconds ?
  • 60 km
  • 30 km
  • 45 km
  • None of these
What is the distance in space between (1,0,5) and (3,6,3)?
  • 4
  • 6
  • 211
  • 214
  • 12
A triangle ABC is placed so that the midpoints of its sides are on the x,y and z axes respectively. Lengths of the intercepts made by the plane containing the triangle on these axes are respectively α,β,γ, then the coordinates of the centroid of the triangle ABC are
  • (α3,β3,γ3)
  • (α3,β3,γ3)
  • (α3,β3,γ3)
  • (α3,β3,γ3)
Point A is a+2b, and a divides AB in the ratio 2 :The position vector of B is
  • 2ab
  • b2a
  • a3b
  • b
D(2,1,0),E(2,0,0),F(0,1,0) are mid point of the sides BC,CA,AB of Δ ABC respectively, The the centroid of ΔABC is
  • (13,13,13)
  • (43,23,0)
  • (13,13,13)
  • (23,13,13)
If P(x,y,x) is a point on the line segment joining Q(2,2,4) and R(3,5,6) such that the projection 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
There are three points with position vectors 2a+3b+5c,a+2b+3c and7ac. What is the relation between the three points?
  • Collinear
  • Forms a triangle
  • In different plane
  • None of the above
The plane ax+by+cz+d=0 divides the line joining the points (x1,y1,z1) and (x2,y2,z2) in the ratio
  • (ax1+by1+cz1+d)(ax2+by2+cz2+d)
  • (ax1+by1+cz1+d)(ax2+by2+cz2+d)
  • ax1x2+by1y2+cz1z2d2
  • None of these
The set of points in space 4 inches from a given line and 4 inches from a given point on this line is ______ , if given point lies on the given line.

  • a set consisting of two points
  • a set consisting of four points
  • a set consisting of two circles
  • the empty set
Let  a,b,cϵR such that abc=p and qab=0, where p and q are fixed positive number, then minimum distance of the point (a,b,c) from origin in the three dimensional coordinate system is: 
  • 3(p(q2+1)2q)1/3
  • 3(p(q2+1)q)1/3
  • 3(p)1/3
  • 2(pq)1/2
0:0:1


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