Angle between two vectors - Queen's College, Hong Kong
Angle between two vectors
(1) Vector method
In Diagram 1, let
[pic],
[pic]
then
[pic]
[pic]
[pic] …. (1)
, where [pic].
We see that when (i) [pic]
(ii) [pic].
(2) Co-geom. method
As in the Diagram 2 on the right,
the gradients of OA, OB are
[pic]
[pic]
Assuming [pic],
[pic] [pic]
[pic] , where [pic]. …. (2)
Readers may investigate various cases for which the ( lies.
(3) Check
Please check that (1) and (2)
give the same result, that is,
the following identity holds:
[pic]
[pic]
(4) Further investigations
We use tan to get the formula in (2), can we use other trigo. functions?
Refer to Diagram 2,
[pic]
[pic] …. (3)
It is easy to see that (3) is good to obey the Pythagoras Theorem in Diagram 3.
Readers may check: [pic] gives (1).
(5) Cosine Law
If we apply cosine law for (OAB in Diagram 2, we have
[pic]
[pic] …. (4)
Please check that (4) is equivalent to (1).
-----------------------
(
[pic]
[pic]
[pic]
Diagram 3
Diagram 1
Diagram 2
................
................
In order to avoid copyright disputes, this page is only a partial summary.
To fulfill the demand for quickly locating and searching documents.
It is intelligent file search solution for home and business.
Related download
Related searches
- hong kong net scheme
- hong kong education city limited
- hong kong education city
- hong kong education board
- hong kong college students
- hong kong college of technology
- distance between two vectors calculator
- distance between two vectors linear algebra
- distance between two vectors formula
- angle between two vectors calculator
- calculate angle between two points
- find angle between two vectors