lect_02_ - Vectors and Vector Analysis Scalar...

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Vectors and Vector Analysis •S c a l a r – Representation of a quantity using only a number (e.g., temperature). •V e c t o r –Representat ionofa quantity that has both magnitude and direction (e.g., wind velocity). • Unit Vectors – Vectors with unit length (i.e., magnitude = 1) that are parallel to the coordinate axes. x y z j ˆ k ˆ i ˆ Representing Wind As a Vector N WE S 90° 360° 270° 180° KACY 251339Z 15021G31KT 2 1/2SM +RA BR OVC005 13/12 A2949 knots V 21 = r knots u ° = 30 sin 21 knots u 5 . 10 = knots v ° = 30 cos 21 knots v 2 . 18 = k w j v i u V ˆ ˆ ˆ + +
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Magnitude of a Vector 2 2 2 z y x A A A A + + = r Example: 2 2 2 w v u V + + = r Basic Vector Operations k ˆ A j ˆ A i ˆ A A z y x + + = r Multiplication of a vector by a scalar: () ( ) ( ) k ˆ cA j ˆ cA i ˆ cA A c z y x + + = r (change in magnitude without change in direction)
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k ˆ B j ˆ B i ˆ B B z y x + + = r k ˆ A j ˆ A i ˆ A A z y x + + = r Vector Addition:
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This note was uploaded on 10/25/2011 for the course ENVSCI 324 taught by Professor Broccoli during the Spring '11 term at Rutgers.

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lect_02_ - Vectors and Vector Analysis Scalar...

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