Math Tutoring on Vectors in Space
The xyz-Coordinate System:
We can construct a three-dimensional coordinate system by introducing a third axis called the z-axis. This space is sometimes called R3 in math tutoring. Each point in space is identified by an ordered triple (x, y, z). There are 8 octants rather than 4 quadrants.
The distance between points (x1, y1, z1) and (x2, y2, z2) is given by
The midpoint of a line segment with endpoints (x1, y1, z1) and (x2, y2, z2) is given by
Vectors in Space:
For a vector with initial point (x1, y1, z1) and terminal point (x2, y2, z2), the Unique Position Vector ‘v’ is
The Magnitude or length of ‘v’ is given by
The unit vector in the direction of ‘v’ is given by
Unit Vectors in Space:
A Unit Vector is a vector with magnitude 1.
With Unit Vectors i, j and k any vector in the form can be expressed in the form
Vector Operations in Space:
For vectors and
For Vector and a scalar k:
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1. What is the xyz-Coordinate system?
2. Find the magnitude of a Vector in Space and Unit Vector in Space?
3. Deduce various Vector Operations in Space.
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