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Tuesday, August 27, 2013

How to do Vector Multiplication: Dot and Cross Products

There are times when we will have to multiply two vectors together to define some third quantity.  The strange thing is, there are two ways we can multiply vectors - one where we get a scalar for an answer, and a second where we get a new vector for an answer.  These are called dot (or scalar) products and cross (or vector) products, respectively.

Dot products have two ways of being calculated, and choose the method that makes it easier based on the information given in the problem.  Cross products are a bit more involved and require a 3x3 determinant to figure out the x, y, and z components of the new vector.

Geometrically, dot products multiply the two parallel components of the two vectors.  The formula, if we know the magnitudes of the two vectors, is A dot B = ABcos(theta).  And cross products multiply the two perpendicular components of the two vectors, or A x B = ABsin(theta).  In these definitions, theta is the angle between vectors A and B.

Sunday, August 18, 2013

Electron Micrographs of MANY Things

This is a page of beautiful photos (over 1100) from electron microscopes.  It shows some fascinating structures, and also the beauty and complexities of Nature. Check it out at:

Sunday, August 11, 2013

Pretty Cool Animation of how a Digital Camera Works

This is a short and sweet animation of a Nokia digital camera.  See if you can identify the various steps in the process.