Introduction to Three Dimensional Geometry — Class 11 Mathematics
Mathematics · Chapter 11
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Chapter summary
Locating a point in space requires three mutually perpendicular coordinate axes — the
Coordinate axes and coordinate planes in spaceOctantsCoordinates of a point in spaceSign conventions and octant identificationDistance between two pointsApplications: collinearity and figures
Key ideas & terms
- Coordinate axes in space
- Three mutually perpendicular lines — the
, and -axes — meeting at the origin. - Coordinate planes
- The
, and planes determined by pairs of axes. - Octants
- The eight parts into which the three coordinate planes divide space.
- Coordinates of a point
- An ordered triplet
of perpendicular distances from the , , planes. - Origin
- The point
where the three axes intersect. - Distance formula
.
Extra questions & answers
How many coordinates locate a point in space and why?
Three coordinates
Into how many octants do the coordinate planes divide space?
Eight octants, formed by the three coordinate planes
Give the coordinates of a point on the
A point on the
State the distance formula in three dimensions.
Find the distance between
What is the distance of
Name the octant in which
With
How do you test whether three points are collinear in space?
Compute the three pairwise distances; the points are collinear iff the sum of two of them equals the third.
Coordinates of the origin and the form of a point on the
The origin is
If the centroid of triangle
Using the centroid average for each coordinate gives