3.3_3.4_3.5

3.3_3.4_3.5 - MATH1850U/2050U: Chapter 3 cont. 1 EUCLIDEAN...

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MATH1850U/2050U: Chapter 3 cont. .. 1 EUCLIDEAN VECTOR SPACES cont. .. Orthogonality (Section 3.3; pg. 143) Recall: In the previous section, we found the relationship v u v u 1 cos Definition: Two vectors u and v in n R are called orthogonal (or perpendicular ) if 0 v u . Example: Are any of the given vectors orthogonal to one another? Theorem (Projections): If u and a are vectors in 2-space or 3-space and if 0 a , then the vector component of u along a is a a a u u 2 proj a and the vector component of u orthogonal to a is given by a a a u u u u 2 proj - a . Example: Given , find a) the vector component of u along a b) the vector component of u orthogonal to a .
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MATH1850U/2050U: Chapter 3 cont. .. 2 In section 3.2, we found that many theorems about vectors in R 2 and R 3 hold in n R ...here’s another example of such a generalization. Theorem (Pythagorean Theorem in
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This note was uploaded on 10/12/2011 for the course MATH 1020 taught by Professor Paulatu during the Spring '11 term at UOIT.

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3.3_3.4_3.5 - MATH1850U/2050U: Chapter 3 cont. 1 EUCLIDEAN...

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