Engineering Calculus Notes 66

Engineering Calculus Notes 66 - v = v w b w b . (1.19) This...

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54 CHAPTER 1. COORDINATES AND VECTORS But then the distance formula says that 1 = | −→ u | = r cos 2 α + cos 2 β + cos 2 γ and squaring both sides yields Equation ( 1.18 ). Scalar Projection: The projection proj −→ w −→ v of the vector −→ v in the direction of the vector −→ w is itself a vector; a related quantity is the scalar projection of −→ v in the direction of −→ w , also called the component of −→ v in the direction of −→ w . This is deFned as comp −→ w −→ v = b −→ v b cos θ where θ is the angle between −→ v and −→ w ; clearly, this can also be expressed as −→ v · −→ u , where −→ u := −→ w b −→ w b is the unit vector parallel to −→ w . Thus we can also write comp −→ w −→
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Unformatted text preview: v = v w b w b . (1.19) This is a scalar, whose absolute value is the length of the vector projection, which is positive if proj w v is parallel to w and negative if it points in the opposite direction. Exercises for 1.4 Practice problems: 1. or each pair of vectors v and w below, Fnd their dot product, their lengths, the cosine of the angle between them, and the (vector) projection of each onto the direction of the other: (a) v = (2 , 3), w = (3 , 2) (b) v = (2 , 3), w = (3 , 2)...
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This note was uploaded on 10/20/2011 for the course MAC 2311 taught by Professor All during the Fall '08 term at University of Florida.

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