Prove that the absolute value of a dot product is less than or equal t

AI Thread Summary
To prove that |a•c| ≤ |a||c| for vectors a and c, one can start by expressing the dot product in terms of the magnitudes and the cosine of the angle between them: a•c = |a||c|cos(θ). The absolute value of the dot product, |a•c|, can then be rewritten as |a||c| |cos(θ)|. Since the maximum value of |cos(θ)| is 1, it follows that |a•c| is always less than or equal to |a||c|. This geometric interpretation provides a clear justification for the inequality.
speny83
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Homework Statement



That is prove that |a•c|≤|a||c| for any vector a=<a1,a2,a3> & c=<c1,c2,c3>


Homework Equations





The Attempt at a Solution



I really don't have much of an attempt at the solution. I am not sure where to start. I can kind of justify it in my mind by saying the sum of two magnitudes will always be a positive number and if 1 of the the a1 c1 etc where negative it could bring the value down but that is no where near a proof.

Where does one even begin to start justifying this?
 
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As always, start out by writing down everything relevant that you know. What is |a•c|? What are |a| and |c|? If you write them out, you will have some algebra to manipulate.
 
lbix asked a perfectly reasonable question. Do you know an expression for the magnitude of the dot product of two vectors? Do you know, for example, what the dot product between two vectors signifies geometrically?
 

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