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"Nothing in life is to be feared, it is only to be understood." ..."Marie Curie 1867-1934, Polish born French Physicist, Twice Nobel Prize Winner- Physics and Chemistry)"

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 Author Topic: projection of a vector: inner product A‧B, and cross productor AXB  (Read 8723 times) 0 Members and 1 Guest are viewing this topic. Click to toggle author information(expand message area).
Fu-Kwun Hwang
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Posts: 3086

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

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 $\vec{B}$ 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 $\vec{B}$

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"Nothing in life is to be feared, it is only to be understood." ..."Marie Curie 1867-1934, Polish born French Physicist, Twice Nobel Prize Winner- Physics and Chemistry)"