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June 4th, 2012, 08:14 PM  #1 
Member Joined: Jun 2010 Posts: 35 Thanks: 0  The projection of the vector
For the give vector and , find the projection of vector in . Please include a step by step solution. 
June 5th, 2012, 05:49 AM  #2  
Math Team Joined: Dec 2006 From: Lexington, MA Posts: 3,267 Thanks: 408  Re: The projection of the vector Hello, Phatossi! Quote: [color=beige]. . [/color]  
June 7th, 2012, 07:47 AM  #3 
Math Team Joined: Sep 2007 Posts: 2,409 Thanks: 6  Re: The projection of the vector
Draw a picture: The vectors a and b are two line segments joined at their "tails". Drop a perpendicular from the tip of a to b and you have a right triangle with hypotenuse of length a. Call the angle between the two vectors "". Then the leg of that triangle, lying along vector b, has length . Since the dot product of two vectors, a and b, can be written as , the scalar projection of a on b can be written . To get the vector projection of a on b, multiply that by the unit vector in the direction of b: , the formula soroban gives.


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