Coordinate axes and coordinate planes in 3d space - class-XII
coordinate axes and coordinate planes in 3d space
Questions
The coordinate of any point, which lies in $xy$ plane , is
- $(x,0,y)$
- $(x,x,0)$
- $(x, 0, x)$
- $(y,0,x)$
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
An ordered triplet corresponds to ___________ in three dimensional space.
- three points
- a unique point
- a point in each octant
- infinite number of points
$(-1,-5,-7)$ lies in Octant
- I
- VII
- V
- III
The number of dimension, a point has :
- 0
- 1
- 2
- 3
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)
The graph of the equation $y^{2}+z^{2}=0$ in three dimensional space is
- x- axis
- y- axis
- z- axis
- yz-plane
The foot of the perpendicular from the point $A(7, 14, 5)$ to the plane $2x+4y-z=2$ is?
- $(3, 1, 8)$
- $(1, 2, 8)$
- $(3, -3, 5)$
- $(5, -3, -4)$
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:
- $A,B,C,D$
- $B,C,D,A$
- $C,D,A,B$
- $D,C,B,A$
Graph $x^2+y^2=4$ in 3D looks like
- Circle
- Cylinder
- Hemisphere
- Sphere
The point $(0 , -2 , 5)$ lies on the
- z axis
- x axis
- xy plane
- yz plane
- xz plane
The coordinates of any point, which lies in $yz$ plane, are
- $(x,y,y)$
- $(0,y,y)$
- $(0,y,x)$
- $(x,y,z)$
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
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
The planes $2x-y+4z=5$ and $5x-2.5y+10z=6$ are
- Parallel
- Perpendicular
- Intersect
- intersect $x$ axis
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 $(0, 0)$
The point $(3, 0, -4)$ lies on the
- Y-axis
- Z-axis
- XY-plane
- XZ-plane
- YZ-plane
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
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
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