# capa3 - 1 Make sure you understand the difference between a...

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1) Make sure you understand the difference between a vector and the magnitude of a vector. In the following, consider vectors in 2 dimensions: The magnitude of V 3 = V 1 + V 2 depends on the orientation of the vectors V 1 and V 2 ! Examples: | V 3 |=|V 1 |+|V 2 | | V 3 |=|V 1 |-|V 2 | V 1 V 2 V 2 V 1 V 3 V 3 | V 3 |<|V 1 |+|V 2 | V 2 V 1 V 3 2, 3, 4) Remember: A - B = A + ( - B ) If you know the components Ax, Ay and Bx, By of the vectors A and B , then you get the components Cx and Cy of the vector C = A + B from: Cx = Ax+Bx, and Cy = Ay + By. If you know the components Ax and Ay of a vector A then you know its magnitude | A |: | A | = squareroot of (Ax 2 + Ay 2 ) You know this already from geometry: The ‘Pythagorean relation’: c a b c 2 = a 2 + b 2 (think of a and b as the x and y components of a vector along c with magnitude c) β a b c a = c * cos β (‘a’ is the cozy side of β ) b = c * sin β Use this information to solve problems 2, 3, and 4.

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5. Remember: The magnitude of a vector V is the ‘length’ of the vector. Above you find how to calculate the magnitude in 2 dimensions (use the Pythagorean relation | V | = x 2 + y 2 . In 3 dimensions you can simply use | V | = x 2 + y 2 + z 2 (see text book.) If you are given a vector as V = x* i + y* j + z* k , then x,y,z are the x, y, and z components of the vector. The magnitude |
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## This note was uploaded on 11/07/2010 for the course PHYS 1120 taught by Professor Rogers during the Spring '08 term at Colorado.

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capa3 - 1 Make sure you understand the difference between a...

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