Coordinates in 3d - class-XI

Question 1 Multiple Choice (Single Answer)

The coordinates of any point, which lies on $x$ axis are

$(0,x,0)$
$(x,0,0)$
$(x,x,0)$
$(x,x,x)$

Question 2 Multiple Choice (Single Answer)

A point at which all the three perpendicular coordinate axes meets is known as

Meeting point
Origin
Triple point
None of these

Question 3 Multiple Choice (Single Answer)

If point $p$ lies in first octant, then the sign of $x-$ coordinate will always be

$+$
$-$
$x$ coordinate is always $0$
$x$ coordinate can be $+$ or $-$

Question 4 Multiple Choice (Single Answer)

Which one of the following 3D shapes does not have a vertex?

Sphere
Pyramid
Prism
Cone

Question 5 Multiple Choice (Single Answer)

Examine if the following is true statement.
The cube can cast a shadow in the shape of a rectangle.

True
False

Question 6 Multiple Choice (Single Answer)

Examine if the following is true statement.
The cube can cast a shadow in the shape of a hexagon.

True
False

Question 7 Multiple Choice (Single Answer)

Name three undefined terms.

Point
Line
Plane
All of the above

Question 8 Multiple Choice (Single Answer)

Platonic solids are regular Polyhedra.

True
False

Question 9 Multiple Choice (Single Answer)

The coordinate of any point, which lies in $xy$ plane , is

$(x,0,y)$
$(x,x,0)$
$(x, 0, x)$
$(y,0,x)$

Question 10 Multiple Choice (Single Answer)

In three dimensions, the coordinate axes of a rectangular cartesian coordinate system are

three mutually parallel lines
three mutually perpendicular lines
two mutually perpendicular lines and any two parallel
None of these

Question 11 Multiple Choice (Single Answer)

Who gave the systematic development of analytical geometry for the first time?

Leonard Euler
J. Bernoulli
Rene' Descartes
Pierre Fermat

Question 12 Multiple Choice (Single Answer)

An ordered triplet corresponds to ___________ in three dimensional space.

three points
a unique point
a point in each octant
infinite number of points

Question 13 Multiple Choice (Single Answer)

$(-1,-5,-7)$ lies in Octant

I
VII
V
III

Question 14 Multiple Choice (Single Answer)

The number of dimension, a point has :

0
1
2
3

Question 15 Multiple Choice (Single Answer)

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)

Question 16 Multiple Choice (Single Answer)

The graph of the equation $y^{2}+z^{2}=0$ in three dimensional space is

x- axis
y- axis
z- axis
yz-plane

Question 17 Multiple Choice (Single Answer)

The points $(3,\ 2,\ 0),\ (5,\ 3,\ 2)$ and $(-9,\ 6,\ -3)$, are the vertices of a triangle $ABC.AD$ is the internal bisector of $\angle\ BAC$ which meets $BC$ at $D$. Then the co-ordinates of $D$, are

$\left[ {\dfrac{{17}}{{16}},\ \dfrac{{57}}{{16}},\ \dfrac{{19}}{8}} \right]$
$\left[ {\dfrac{{19}}{{8}},\ \dfrac{{57}}{{16}},\ \dfrac{{17}}{16}} \right]$
$\left[0,\ 0,\ {\dfrac{{17}}{{16}}}\right]$
$\left[{\dfrac{{17}}{{16}}},\ 0,\ 0\right]$

Question 18 Multiple Choice (Single Answer)

The foot of the perpendicular from the point $A(7, 14, 5)$ to the plane $2x+4y-z=2$ is?

$(3, 1, 8)$
$(1, 2, 8)$
$(3, -3, 5)$
$(5, -3, -4)$

Question 19 Multiple Choice (Single Answer)

In geometry, we take a point, a line and a plane as undefined terms.

True
False
Ambiguous
Data Insufficient

Question 20 Multiple Choice (Single Answer)

Arrange the points: $\mathrm{A}(1,2-3), \mathrm{B}(-1,2,-3), \mathrm{C}(-1,-2-3)$ and $\mathrm{D}(1,-2, -3)$ in the increasing order of their octant numbers:

$A,B,C,D$
$B,C,D,A$
$C,D,A,B$
$D,C,B,A$

Octant	$I$	$II$	$III$	$IV$	$V$	$VI$	$VII$	$VIII$
Signs:	$+,+,+$	$-,+,+$	$-,-,+$	$+,-,+$	$+,+,-$	$-,+,-$	$-,-,-$	$+,-,-$

Question 21 Multiple Choice (Single Answer)

Graph $x^2+y^2=4$ in 3D looks like

Circle
Cylinder
Hemisphere
Sphere

Question 22 Multiple Choice (Single Answer)

The point $(0 , -2 , 5)$ lies on the

z axis
x axis
xy plane
yz plane
xz plane

Question 23 Multiple Choice (Multiple Answers)

The coordinates of any point, which lies in $yz$ plane, are

$(x,y,y)$
$(0,y,y)$
$(0,y,x)$
$(x,y,z)$

Question 24 Multiple Choice (Single Answer)

An equation of sphere with centre at origin and radius $r$ can be represented as

$x^2+y^2+z^2=r$
$x^2+y^2+z^2=r^2$
$x^2+y^2+z^2=2r^2$
None of the above

Question 25 Multiple Choice (Single Answer)

The equation of plane passing through $(-1,0,-1)$ parallel to $xz$ plane is

$y=-2$
$y=0$
$-x-z=0$
None of the above

Question 26 Multiple Choice (Single Answer)

The planes $2x-y+4z=5$ and $5x-2.5y+10z=6$ are

Parallel
Perpendicular
Intersect
intersect $x$ axis

Question 27 Multiple Choice (Single Answer)

In a three-dimensional space, the equation $3x - 4y = 0$ represents.

A plane containing $Z-axis$
A plane containing $X-axis$
A plane containing $Y-axis$
Passing through $(0, 0)$

Question 28 Multiple Choice (Single Answer)

The point $(3, 0, -4)$ lies on the

Y-axis
Z-axis
XY-plane
XZ-plane
YZ-plane

Question 29 Multiple Choice (Multiple Answers)

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 $y$ in a $zx$ plane is non-zero.
Value of $z$ in a $xy$ plane is zero.
None of the above

Question 30 Multiple Choice (Single Answer)

There are three points with position vectors $ -2a+3b+5c, a+2b+3c $ and$ 7a-c$. What is the relation between the three points?

Collinear
Forms a triangle
In different plane
None of the above

Question 31 Multiple Choice (Single Answer)

The coordinates of the point where the line through $(3, -4, -5)$ and $(2, -3, 1)$ crosses the plane passing through three points $(2, 2, 1),(3, 0, 1)$ and $(4, -1, 0)$ is

$(1, 2, 7)$
$(-1, 2, -7)$
$(1, -2, 7)$
None of these

Coordinates in 3d - class-XI

Questions