2224-Sec10_5-HWT

# 2224-Sec10_5-HWT - Mat h 22 24 Multiva ri a ble C alc ul us...

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Math 2224 Multivariable Calculus – Sec. 10.5: Lines and Planes in Space Abbreviations : wrt = with respect to ! = for all ! = there exists ! = therefore Def n = definition Th m = Theorem sol n = solution ! = perpendicular iff or ! = if and only if pt = point fn = function eq = equation ! =is an element of st = such that I. Review Let ! v = v =<a,b,c>=a i +b j +c k Magnitude=length=norm v = v = a 2 + b 2 + c 2 The unit vector in the same direction as v = v v Vectors a and b are parallel if a x b =0 and perpendicular (orthogonal, normal) if a ! b = 0 . The vector a x b is orthogonal to both a and b . II. Lines A. Lines in 2-Space A line in two-dimensional space is determined when a point and a slope (direction) are given. B. Lines in 3-Space 1. A line L three-dimensional space is determined by a point P 0 ( x 0 , y 0 , z 0 ) and the direction of L, which is given by a vector v that is parallel to L . 2. Vector equation for a line L : r = r 0 + tv a. A vector equation for the line L through P 0 ( x 0 , y 0 , z 0 ) parallel to v =< a, b, c > is r ( t ) = r 0 + tv , ! " < t < " , where r is the position vector of a point P ( x , y , z ) on

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## This note was uploaded on 04/05/2008 for the course MATH 2224 taught by Professor Mecothren during the Spring '03 term at Virginia Tech.

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2224-Sec10_5-HWT - Mat h 22 24 Multiva ri a ble C alc ul us...

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