Coordinate Axes in Three Dimensional Space

Q.

The direction cosines of Y-axis are:

1. 0, 1, 0

2. 1, 0, 0

3. 1, 1, 1

4. 0, 0, 1

Q. A variable plane at a constant distance p from origin meets the co-ordinate axes in A, B, C. Through these points planes are drawn parallel to co-ordinate planes.Then locus of the point of intersection is

1. $\frac{1}{x^2}+\frac{1}{y^2}+\frac{1}{z^2}=\frac{1}{p^2}$
2. $x^2+y^2+z^2=p^2$
3. $x+y+z=p$
4. $\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=p$

Q. Whats the angle between a diagonal of a cube and the diagonal of face of the cube

Q.

If the perpendicular distance of a point $P$ from the $x-axis$ is $5$ units and the foot of the perpendicular lies on the negative direction of $x-axis$, then the point $P$ has

1. $x-$ coordinate $=-5$

2. $y-$coordinate $=$$5$ only

3. $y-$ coordinate $=-5$ only

4. $y-$coordinate $=-5$ or $5$

Q.

What is the locus of the point for which y = 0, z = 0?

1. x-axis

2. y-axis

3. z-axis

4. yz-plane

Q. a focus of an ellipse is at the origin. the directrix is the line x=4 and e is 1/2. then length of semi major axis

Q.

A point (x, y, z) moves parallel to x-axis. Which of the three variable x, y, z remain fixed

1. z and x

2. x

3. y and z

4. x and y

Q. Find the octant in which the points $(-3,1,2)\text{and}(-3,1,-2)$ lie.

Q. If the axis of a parabola is horizontal and it passes through the points (0, 0), (0, -1) and (6, 1), then its equation is

1. 
2. None of these
3. 
   
4. 

Q. The three Coordinate axes divides the space into parts.

1. 8
2. 16
3. 2
4. 4

Q.

Find the area of the region bounded by the curve y² = x and the lines x = 1, x = 4 and the x-axis.

Q.

If a line in the space makes angles $\alpha ,\beta$ and $\gamma$ with the coordinates axes, the $\cos 2\alpha +\cos 2\beta +\cos 2\gamma +{\sin }^2\alpha +{\sin }^2\beta +{\sin }^2\gamma$equals

1. $-1$

2. $0$

3. $1$

4. $2$

Q.

$\mathit{Q}\mathit{u}\mathit{e}\mathit{s}\mathit{t}\mathit{i}\mathit{o}\mathit{n}\mathbf{}\mathit{N}\mathit{o}\mathbf{}\mathbf{2}\mathbf{:}$

If $21,a,b,and-3$$18$ are in AP, then find the value of $(a+b).$

Q.

How do you find the maximum and minimum of a feasible region $?$

Q. A plane makes intercepts −6, 3, 4 respectively on the coordinate axes. Find the length of the perpendicular from the origin on it. [CBSE 2014]

Q. The equation to the locus of a point "P" for which the distance from "P" to (6, 5) is triple the distance from "P" to x-axis is.

Q. What is a 4rth dimensional figure ? How can we visualise them ?

Q. If a line in the space makes angles $\alpha ,\beta$ and $\gamma$ with the coordinate axes, then $\cos 2\alpha +\cos 2\beta +\cos 2\gamma +{\sin }^2\alpha +{\sin }^2\beta +{\sin }^2\gamma =$

1. $-1$
2. $0$
3. $1$
4. $2$

Q. Imagine the YZ plane in front of you. The z-axis is towards your right and the y-axis points vertically up. Then the x-axis is .

1. out of the plane
2. into the plane
3. towards the left
4. vertically downwards

Q.

An arch is in the form of a parabola with its axis vertical. The arch is 10 m high and 5 m wide at the base. How wide is it 2 m from the vertex of the parabola?

Q. A diet is to contain at least $80$ units of vitamin $A$ and $100$ units of minerals. Two foods $F_1$ and $F_2$ are available. Food $F_1$ costs $\text{Rs}4$ per unit and food $F_2$ costs $\text{Rs}6$ per unit. One unit of food $F_1$ contains $2$ units of vitamin $A$ and $4$ units of minerals and one unit of $F_2$ contains $4$ units of vitamin $A$ and $3$ units of minerals. Then for minimum cost of diet which will produce the required diet, which of the following is correct?

1. The minimum cost of diet is $\text{Rs}136$
2. quantity of food $F_1$ is $16$ units
3. quantity of food $F_1$ is $12$ units
4. optimal solution is not possible.

Q.

The area bounded by the curve y² = 16x, x = 1, x = 3 and X-axis is:

1. 

2. 

3. 

4. 

Q.

A bicycle wheel is represented in a coordinate plane with the center of the wheel at the origin. Reflectors are placed on the bicycle wheel at points $(7,4)$ and $(-5,-6)$. After a bike ride, the reflectors have rotated $90°$ counterclockwise about the origin. What are the locations of the reflectors at the end of the bike ride?

Q.

Area of the region bounded by the curve y² = 4x, y-axis and the line y = 3 is

A. 2

B.

C.

D.

Q. Fill in the blanks:​
v). $7-4=$ and 7ab - 4ab =

Q. The opposite vertices of a rectangular parallelepiped are (-1, 2, 6) and (2, 7, 10). The planes of the parallelepiped are parallel to coordinate plane. Find the volume of the parallelepiped

Q. Find the direction cosines of a line which makes equal angles with the coordinate axes.

Q.

Find direction cosines of y-axis.

1. 0, 0, 1

2. 1, 0, 0

3. 0, 1, 0

4. 0, 0, 0

Q.

All the points on the x- axis have
[MP PET 1988]

1. y=0, z=0

2. x=0

3. y=0

4. x=0, y=0

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

1. Sphere
2. Pyramid
3. Prism
4. Cone