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June 4th, 2012, 08:14 PM   #1
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The projection of the vector

For the give vector and , find the projection of vector in .

Please include a step by step solution.
Phatossi is offline  
June 5th, 2012, 05:49 AM   #2
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Re: The projection of the vector

Hello, Phatossi!


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June 7th, 2012, 07:47 AM   #3
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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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