English

Coordinate planes divide the space into ______ octants.

Advertisements
Advertisements

Question

Coordinate planes divide the space into ______ octants.

Fill in the Blanks
Advertisements

Solution

Coordinate planes divide the space into eight octants.

shaalaa.com
  Is there an error in this question or solution?
Chapter 11: Introduction to Three Dimensional Geometry - EXERCISE 11.1 [Page 211]

APPEARS IN

NCERT Mathematics [English] Class 11
Chapter 11 Introduction to Three Dimensional Geometry
EXERCISE 11.1 | Q 4. (iii) | Page 211

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

Name the octants in which the following points lie: (5, 2, 3)


Name the octants in which the following points lie: 

(–5, –4, 7) 


Name the octants in which the following points lie: 

(–5, –3, –2) 


Name the octants in which the following points lie: 

(–7, 2 – 5)


Find the image  of:

 (5, 2, –7) in the xy-plane.


Find the image  of: 

 (–4, 0, 0) in the xy-plane. 


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.


Planes are drawn parallel to the coordinate planes through the points (3, 0, –1) and (–2, 5, 4). Find the lengths of the edges of the parallelepiped so formed.


Find the points on z-axis which are at a distance \[\sqrt{21}\]from the point (1, 2, 3). 


Prove that the point A(1, 3, 0), B(–5, 5, 2), C(–9, –1, 2) and D(–3, –3, 0) taken in order are the vertices of a parallelogram. Also, show that ABCD is not a rectangle.


Find the coordinates of the point which is equidistant  from the four points O(0, 0, 0), A(2, 0, 0), B(0, 3, 0) and C(0, 0, 8).


Are the points A(3, 6, 9), B(10, 20, 30) and C(25, –41, 5), the vertices of a right-angled triangle?


Verify the following: 

 (0, 7, –10), (1, 6, –6) and (4, 9, –6) are vertices of an isosceles triangle.


Verify the following: 

(0, 7, 10), (–1, 6, 6) and (–4, 9, –6) are vertices of a right-angled triangle.


Verify the following:

 (5, –1, 1), (7, –4,7), (1, –6,10) and (–1, – 3,4) are the vertices of a rhombus.


Show that the points A(1, 2, 3), B(–1, –2, –1), C(2, 3, 2) and D(4, 7, 6) are the vertices of a parallelogram ABCD, but not a rectangle.


Find the ratio in which the sphere x2 + y2 + z2 = 504 divides the line joining the points (12, –4, 8) and (27, –9, 18).


Write the coordinates of the foot of the perpendicular from the point (1, 2, 3) on y-axis.


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


The ratio in which the line joining (2, 4, 5) and (3, 5, –9) is divided by the yz-plane is


The ratio in which the line joining the points (a, b, c) and (–a, –c, –b) is divided by the xy-plane is


The coordinates of the foot of the perpendicular drawn from the point P(3, 4, 5) on the yz- plane are


The length of the perpendicular drawn from the point P(a, b, c) from z-axis is 


If a line makes an angle of 30°, 60°, 90° with the positive direction of x, y, z-axes, respectively, then find its direction cosines.


Find 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)


Find the co-ordinates of the foot of perpendicular drawn from the point A(1, 8, 4) to the line joining the points B(0, –1, 3) and C(2, –3, –1).


If α, β, γ are the angles that a line makes with the positive direction of x, y, z axis, respectively, then the direction cosines of the line are ______.


A line makes equal angles with co-ordinate axis. Direction cosines of this line are ______.


Find the angle between the lines whose direction cosines are given by the equations l + m + n = 0, l2 + m2 – n2 = 0


Two systems of rectangular axis have the same origin. If a plane cuts them at distances a, b, c and a′, b′, c′, respectively, from the origin, prove that

`1/a^2 + 1/b^2 + 1/c^2 = 1/(a"'"^2) + 1/(b"'"^2) + 1/(c"'"^2)`


Find the length and the foot of perpendicular from the point `(1, 3/2, 2)` to the plane 2x – 2y + 4z + 5 = 0.


If the directions cosines of a line are k, k, k, then ______.


The area of the quadrilateral ABCD, where A(0, 4, 1), B(2,  3, –1), C(4, 5, 0) and D(2, 6, 2), is equal to ______.


The vector equation of the line through the points (3, 4, –7) and (1, –1, 6) is ______.


The cartesian equation of the plane `vecr * (hati + hatj - hatk)` is ______.


The unit vector normal to the plane x + 2y +3z – 6 = 0 is `1/sqrt(14)hati + 2/sqrt(14)hatj + 3/sqrt(14)hatk`.


The intercepts made by the plane 2x – 3y + 5z +4 = 0 on the co-ordinate axis are `-2, 4/3, - 4/5`.


If the foot of perpendicular drawn from the origin to a plane is (5, – 3, – 2), then the equation of plane is `vecr.(5hati - 3hatj - 2hatk)` = 38.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×