Tuesday, March 20, 2007

Lesson 10-3-Vectors in Space

The Overview of the lesson

This Image on the left is referred to as an Octant.

Octant-The xy-plane, yz-plane, and xz-plane divided into 8 regions.

The region in which all the three variables are positive is called first octant.

The X axis- i variable, the Y axis- j variable, and the z axis- k variable. The variables are used for unit vectors in the x-, y-, and z- direction respectively.

To finding the magnitude is similar to finiding the 2-dimensional magnitude.

Example of this lesson

Example #1- Find the length of vector P. Vector P=4i+5j+9k

Magnitude (length)- square root of (4^2 + 5^2 + 9^2)


Example #2- Find the displacement vector of point A(9,3,14) to point B(4,11,5).

One always subtracts from head to tail.

(4i+11j+5k) - (9i+3j+14k)= -5i+8j-9k=Displacement vector from A to B.

Example #3- Find the positon vector to the point 70% of the way from point A(9,3,14) to point B(4,11,5).

Position vector is A+.7(AB)

9i+3j+14k + .7(-5i+3j-9k)= 5.5i+5.1j+7.7k

Additional source

Additional Source that will help is found online on Wikipedia. Type in the search vectors and one will find online assitance.

Allison your next up-good luck

I hope my UCLA Bruins win it all this March in the tornument. This is a picture that examplifies UCLA Basketball.


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