NTNUJAVA Virtual Physics LaboratoryEnjoy the fun of physics with simulations! Backup site http://enjoy.phy.ntnu.edu.tw/ntnujava/
February 20, 2020, 04:06:27 am

A man paints with his brains and not with his hands. ..."Michelangelo (1475-1564, Italian sculptor, painter, architect and poet)"

 Pages: [1]   Go Down
 Author Topic: projection of a vector: inner product A‧B, and cross productor AXB  (Read 8361 times) 0 Members and 1 Guest are viewing this topic. Click to toggle author information(expand message area).
Fu-Kwun Hwang
Hero Member

Offline

Posts: 3085

 « Embed this message on: November 26, 2010, 01:23:48 pm » posted from:,,Taiwan

The following applet shows
1. The inner product(which is a scale) is defined as $\vec{A}\cdot\vec{B}=|\vec{A}|\,|\vec{B}|\cos\theta$ ,
So projection of vector $\vec{A}$ into another direction math_failure (math_image_error): \vec{B} can be calculated as $\vec{C}=(\vec{A}\cdot \hat{B}) \hat{B}=(\vec{A}\cdot\frac{\vec{B}}{|\vec{B}|})\frac{\vec{B}}{|\vec{B}|}$

2. The cross product $\vec{D}=\vec{A}\times\vec{B}$, $|\vec{D}|=|\vec{A}|\, |\vec{B}| \sin\theta$ where $\theta$ is the angle between $\vec{A}$ and $\vec{B}$

Embed a running copy of this simulation

Embed a running copy link(show simulation in a popuped window)
Full screen applet or Problem viewing java?Add http://www.phy.ntnu.edu.tw/ to exception site list