Unformatted text preview:  âˆ’â†’ v  and  âˆ’â†’ w  are both nonzero ( i.e. , âˆ’â†’ v n = âˆ’â†’ n = âˆ’â†’ w ) then âˆ’â†’ v Â· âˆ’â†’ w = 0 precisely when cos Î¸ = 0, and this is the same as saying that âˆ’â†’ v is perpendicular to âˆ’â†’ w (denotedâ†’ v âŠ¥â†’ w ). But if either âˆ’â†’ v or âˆ’â†’ w is âˆ’â†’ 0 , then clearly âˆ’â†’ v Â· âˆ’â†’ w = 0 by either side of Equation ( 1.17 ). 3. This is just (1) when âˆ’â†’ v = âˆ’â†’ w , which in particular means Î¸ = 0, or cos Î¸ = 1. 4. This follows from Equation ( 1.15 ) by substitution: proj âˆ’â†’ w âˆ’â†’ v = p  âˆ’â†’ v   âˆ’â†’ w  cos Î¸ P âˆ’â†’ w = Â±  âˆ’â†’ v  âˆ’â†’ w   âˆ’â†’ w  2 cos Î¸ Â² âˆ’â†’ w = p âˆ’â†’ v Â· âˆ’â†’ w âˆ’â†’ w Â· âˆ’â†’ w P âˆ’â†’ w....
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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.
 Fall '08
 ALL
 Calculus, Vectors, Dot Product

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