CBSE Questions for Class 11 Engineering Maths Introduction To Three Dimensional Geometry Quiz 7 - MCQExams.com

The planes 2xy+4z=52xy+4z=5 and 5x2.5y+10z=65x2.5y+10z=6 are
  • Parallel
  • Perpendicular
  • Intersect
  • intersect xx axis
The equation of plane passing through (1,0,1)(1,0,1) parallel to xzxz plane is
  • y=2y=2
  • y=0y=0
  • xz=0xz=0
  • None of the above
The distance of the point P(a,b,c)P(a,b,c) from the xx-axis is.
  • b2+c2b2+c2
  • a2+c2a2+c2
  • a2+b2a2+b2
  • aa
If a line OPOP of length rr (Where 'OO' is the origin) makes an angle αα with x-axis and lies on the xz-plane, then what are the coordinates of PP?
  • (rcosα,0,rsinα)(rcosα,0,rsinα)
  • (0,0,rsinα)(0,0,rsinα)
  • (rcosα,0,0)(rcosα,0,0)
  • (0,0,rcosα)(0,0,rcosα)
Which of the following is true for a plane?
  • A locus is called a plane if the line joining any two arbitrary points on the locus is also a part of the locus.
  • Value of yy in a zxzx plane is non-zero.
  • Value of zz in a xyxy plane is zero.
  • None of the above
Points A(3,2,4),B(335,285,385)A(3,2,4),B(335,285,385), and C(9,8,10)C(9,8,10) are given. The ratio in which BB divides ¯AC¯¯¯¯¯¯¯¯AC is
  • 5:35:3
  • 2:12:1
  • 1:31:3
  • 3:23:2
The locus of a point, which is equidistant from the points (1,1)(1,1) and (3,3)(3,3), is
  • y=x+4y=x+4
  • x+y=4x+y=4
  • x=2x=2
  • y=2y=2
  • y=xy=x
Let OO be the origin and AA be the point (64,0)(64,0). If PP and QQ divide OAOA in the ratio 1:2:31:2:3, then the point PP is
  • (323,0)(323,0)
  • (32,0)(32,0)
  • (643,0)(643,0)
  • (16,0)(16,0)
  • (163,0)(163,0)
The shortest distance between z-axis and the line 
x+y+2z3=0=2x+3y+4z4x+y+2z3=0=2x+3y+4z4, is _____________
  • 11
  • 22
  • 44
  • 33
If z1z1 and z2z2 are zz co-ordinates of the points of trisection of the segment joining the points A(2,1,4),B(1,3,6)A(2,1,4),B(1,3,6) then z1+z2=z1+z2=
  • 11
  • 44
  • 55
  • 1010
In the triangle with vertices A(1,1,2),B(5,6,2)A(1,1,2),B(5,6,2) and C(1,3,1)C(1,3,1) find the altitude n=|BD|n=|BD|.
  • 55
  • 1010
  • 5252
  • 102102
The distance between the X-axis and the point (3,12,5)(3,12,5) is
  • 3
  • 13
  • 14
  • 12
  • 5
The point which divides the line joining the points (1,3,4)(1,3,4) and (4,3,1)(4,3,1) internally in the ratio 2:1,2:1, is 
  • (2,3,3)(2,3,3)
  • (2,3,3)(2,3,3)
  • (52,3,52)(52,3,52)
  • (3,3,2)(3,3,2)
  • (3,3,2)(3,3,2)
The coordinates of the foot of the perpendicular drawn from the point A(1,0,3)A(1,0,3) to the join of the points B(4,7,1)B(4,7,1) and C(3,5,3)C(3,5,3) are
  • (5,7,17)(5,7,17)
  • (57,73,173)(57,73,173)
  • (57,73,173)(57,73,173)
  • (57,73,173)(57,73,173)
If xy -plane and yz-plane divides the line segment joining A(2,4,5) and B(3,5,-4) in the ratio a:b and p:q respectively then value of (ab,pq)(ab,pq)  may be
  • 23122312
  • 7575
  • 712712
  • 21102110
A swimmer can swim 22 km in 1515 minutes in a lake and in a river he can swim a distance of 44 km in 2020 minutes along the stream. If a paper boat is put in the river, then the distance covered by it in 212122 hours will be 
  • 1818 km
  • 1212 km
  • 88 km
  • 1010 km
In a ABCABC, side ABAB has the equation 2x+3y=292x+3y=29 and the side ACAC has the equation x+2y=16x+2y=16. If the mid point of BCBC is (5,6)(5,6), then the equation of BCBC is
  • 2x+y=72x+y=7
  • x+y=1x+y=1
  • 2xy=172xy=17
  • None of these
Plane ax+by+cz=1ax+by+cz=1 intersect axes in A,B,CA,B,C respectively. If G(16,13,1)G(16,13,1) is a centroid of ABCABC then a+b+3c=a+b+3c= _________.
  • 4343
  • 44
  • 22
  • 5656
If xyxyplane and yzyzplane divides the line segment joining A(2,4,5)A(2,4,5) and B(3,5,4)B(3,5,4) in the ratio a:ba:b and p:qp:q respectively then value of (ab+pq)(ab+pq) may be
  • 23122312
  • 7575
  • 712712
  • 21102110
Locus of a point PP which such that PA=PBPA=PB where A=(0,3,2)A=(0,3,2) and B=(2,4,1)B=(2,4,1) is
  • 2x+yz=42x+yz=4
  • x2y+z+1=0x2y+z+1=0
  • 9x2y+4z5=09x2y+4z5=0
  • None of these
Points (5,0,2),(2,6,0),(4,9,6)(5,0,2),(2,6,0),(4,9,6) & (7,3,8)(7,3,8) are vertices of a 
  • Square
  • Rhombus
  • Rectangle
  • Parallelogram
The values of a for which (8,7,a),(5,2,4)(8,7,a),(5,2,4) and (6,1,2)(6,1,2) are collinear , is given by 
  • 22
  • 22
  • 11
  • 11
Given A(3,2,4),B(5,4,6)A(3,2,4),B(5,4,6) & C(9,8,10)C(9,8,10) are collinear. Ratio in which BB divides ACAC
  • 1:21:2
  • 2:12:1
  • 1:21:2
  • None of these
A cube of side 5 has one vertex at the point (1,0,-1), and the three edges from this vertex are, respectively, parallel to the negative x and y axes and positive  z-axis. Find the coordinates of the other vertices of the cube.
  •  (1,0,1)
  •  (0,-1,0)
  •  (0,0,-1)
  • (1,0,0)
If O=(0,0,0),OP=5O=(0,0,0),OP=5 and the d.rs of OP are 1,2,21,2,2 then Px+Py+Pz=Px+Py+Pz=
  • 2525
  • 259259
  • 253253
  • (53,103,103)(53,103,103)
Find the co-ordinates of a point lying on the line x23=y+34=z17 which is at a distance 10 units from (2,3,1).
  • (32,37,71)
  • (28,43,69)
  • (32,37,71)
  • None of these
The ratio in which the join of (1,2,4) and (4,2,1) divided by the XY plane is
  • 1:3
  • 3:1
  • 4:1
  • 1:4
A plane meets the co-ordinate axes in A,B,C such that the centroid of the triangle ABC is the point (p,q,r). The equation of the plane is 
  • xp+yq+zr=0
  • xp+yq+zr=1
  • xp+yq+zr=2
  • none of these
If a point P from where line drawn cuts coordinates axes at A and B (with A on xaxis and B on yaxis ) satisfies αx2PB2+βy2PA2=1, then α+β is
  • 1
  • 2
  • 3
  • 4
The distance between the points (cosθ,sinθ) and (sinθcosθ) is
  • 3
  • 2
  • 2
  • 1
0:0:1


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