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Lec-02 - SCALARS AND VECTORS Learning Objectives After you...

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1 [©2008 RJ Bieniek] S CALARS AND V ECTORS Learning Objectives After you complete the homework associated with this lecture, you should be able to: Know the definitions of scalars , vectors , unit vectors , components of vector , magnitude of a vector , and the conventional symbols for each. Understand vector properties and unit-vector notation. Use “avenue and street” method to determine the sign and magnitude of the components of vectors. Add and subtract vectors. 2 [©2008 RJ Bieniek] Signs in Algebraic Expressions in Sums Let us consider x = 3 a n with a 1 = + | a 1 | ( ˆ a 1 is positive) a 2 = S | a 2 | ( ˆ a 2 is negative) Q UESTION : How would you write out the sum? Correct: Correct: x = 3 a n = a 1 + a 2 A sum is addition Caution Caution : a VERY common algebraic error x = 3 a n = a 1 + S a 2 = a 1 + ( S a 2 ) = a 1 S a 2 Example: a 1 = + 9 and a 2 = S 6 . 3 [©2008 RJ Bieniek] S CALARS Scalar: Mathematical entity that can be fully represented by just a number, either positive or negative, and associated units (if any).
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