11th Grade > Mathematics
INTRODUCTION TO THREE DIMENSIONAL GEOMETRY MCQs
Introduction To Three Dimensional Geometry
Total Questions : 49
| Page 2 of 5 pages
Answer: Option C. -> Octant V
:
C
The x and y coordinates are positive and the z coordinate is negative. Hence, it lies in octantV.
:
C
The x and y coordinates are positive and the z coordinate is negative. Hence, it lies in octantV.
Answer: Option D. -> All of these
:
D
The points which lie on the coordinateaxes or coordinate planes are not part of any octant.
:
D
The points which lie on the coordinateaxes or coordinate planes are not part of any octant.
:
The coordinate planes divide the space into eight octants.
Answer: Option B. -> I, II, V, VI
:
B
The y-coordinate of a point is positive in the octants I, II, V and VI
:
B
The y-coordinate of a point is positive in the octants I, II, V and VI
Answer: Option A. -> (1,0,2)
:
A
Let D(x,y,z) be the fourth vertex of the parallelogram.
The diagonals of a parallelogram bisect each other.
Therefore, the midpoints of AC and BD are the same. Let this be O.
O=(3−12,−1+12,2+22)O=(1,0,2)
Now, O is the midpoint of BD
∴1+x2=1⇒x=12+y2=0⇒y=−24+z2=2⇒z=0
D=(1,0,2)
:
A
Let D(x,y,z) be the fourth vertex of the parallelogram.
The diagonals of a parallelogram bisect each other.
Therefore, the midpoints of AC and BD are the same. Let this be O.
O=(3−12,−1+12,2+22)O=(1,0,2)
Now, O is the midpoint of BD
∴1+x2=1⇒x=12+y2=0⇒y=−24+z2=2⇒z=0
D=(1,0,2)
Answer: Option B. -> externally in the ratio 2:3
:
B
Let the YZ-plane divide theline segment joining the points (4,8,10) and (6,10,-8) in the ratio k:1 at the point P.
The x-coordinate of the point P is given by
x=4+6kk+1
Since P lies on the YZ plane, x=0
⇒4+6k=0⇒k=−23
Hence, the points are divided by the YZ-plane in the ratio 2:3 externally
:
B
Let the YZ-plane divide theline segment joining the points (4,8,10) and (6,10,-8) in the ratio k:1 at the point P.
The x-coordinate of the point P is given by
x=4+6kk+1
Since P lies on the YZ plane, x=0
⇒4+6k=0⇒k=−23
Hence, the points are divided by the YZ-plane in the ratio 2:3 externally
Answer: Option C. -> x2+y2+z2=9
:
C
Let P(x,y,z) be the required point.
According to the given condition
√(x−0)2+(y−0)2+(z−0)2=3⇒x2+y2+z2=9
:
C
Let P(x,y,z) be the required point.
According to the given condition
√(x−0)2+(y−0)2+(z−0)2=3⇒x2+y2+z2=9
:
The distance of the point P(x,y,z) from the x-z plane is
d=|y|=0units
The point lies on the x-z plane.
Answer: Option A. -> (1,5,0)
:
A
For a point on the x-y plane, the z-coordinate is zero and the x and y coordinates are non-zero. Here, (1,5,0) lies on the x-y plane.
:
A
For a point on the x-y plane, the z-coordinate is zero and the x and y coordinates are non-zero. Here, (1,5,0) lies on the x-y plane.
Answer: Option D. -> (-2,-3,-10)
:
D
In the VII th octant, all three coordinates of a point are negative. Here, only the point (-2,-3,-10) lies in the seventh quadrant.
:
D
In the VII th octant, all three coordinates of a point are negative. Here, only the point (-2,-3,-10) lies in the seventh quadrant.
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