Solved

dot product of unit vectors

Posted on 2010-08-22
2
318 Views
Last Modified: 2012-05-10
Hi

This is a bit of a basic question but i was just wondering out of curiosity.

Take i and j as unit vectors. What is i.i and j.j? The answer in both cases is 1. Is this because  you assumed the 2 vectors were on top of each other and so had an ange between then of 0 degrees so the dot product = |i|.|i| . cos(0) = 1

thanks
0
Comment
Question by:andieje
2 Comments
 
LVL 32

Accepted Solution

by:
phoffric earned 500 total points
ID: 33495852
I see you are using the formula v1 . v2 = |v1| |v2| cos (theta), where theta is the angle between v1 and v2.So, if you take the dot product of any two vectors (unit or not) that are pointing in the same direction (i.e., they are parallel), then the angle between them is 0 degrees. v1 . v2 = |v1| |v2| cos (0) =  |v1| |v2| In your case v1 and v2 are unit vectors so  |v1| |v2| = 1*1 = 1If v1 and v2 were parallel, but in opposite directions, then theta = 180 degrees, then v1 . v2 = |v1| |v2| cos (180) =  -|v1| |v2|
0
 

Author Closing Comment

by:andieje
ID: 33495947
thanks
0

Featured Post

Master Your Team's Linux and Cloud Stack!

The average business loses $13.5M per year to ineffective training (per 1,000 employees). Keep ahead of the competition and combine in-person quality with online cost and flexibility by training with Linux Academy.

Question has a verified solution.

If you are experiencing a similar issue, please ask a related question

A Guide to the PMT, FV, IPMT and PPMT Functions In MS Excel we have the PMT, FV, IPMT and PPMT functions, which do a fantastic job for interest rate calculations.  But what if you don't have Excel ? This article is for programmers looking to re…
We are taking giant steps in technological advances in the field of wireless telephony. At just 10 years since the advent of smartphones, it is crucial to examine the benefits and disadvantages that have been report to us.
Although Jacob Bernoulli (1654-1705) has been credited as the creator of "Binomial Distribution Table", Gottfried Leibniz (1646-1716) did his dissertation on the subject in 1666; Leibniz you may recall is the co-inventor of "Calculus" and beat Isaac…
Finds all prime numbers in a range requested and places them in a public primes() array. I've demostrated a template size of 30 (2 * 3 * 5) but larger templates can be built such 210  (2 * 3 * 5 * 7) or 2310  (2 * 3 * 5 * 7 * 11). The larger templa…

777 members asked questions and received personalized solutions in the past 7 days.

Join the community of 500,000 technology professionals and ask your questions.

Join & Ask a Question