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Calc III Ch13 Notes_Part22

# Calc III Ch13 Notes_Part22 - To ﬁnd the normal line we...

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Unformatted text preview: To ﬁnd the normal line we use the gradient terms (aka-the partial derivatives) as the d1rect10n numbers from the pomt P to form parametrlc equatlons: X1 X6 + \—X (X‘)y° 71> 7=yo+" __ \ \. Using the symmetric equations from 11.5 we have 2 '— 2" + X'- X —————9— :— V. 2-— FX (X005, 54 ) :1<—:(.- NOTE: The book does not use this exactly? they use direCtion numbers”, so my answers may look different from the book, but they can be shown to be the same. Ex: Now ﬁnd the normal line for the previous example. Vi: ('Zﬂlkz) : ,L‘ .L 25—; )L PQ’Z‘))/ﬂg> PW .1" 1 4-1-1: :: Y'/ 2- 64“ 1.2-5,};4: ir; 2+3 :3?“ x" 3 4r ﬂ iffE'le" Z+3 64, '” Z " 3 9% Ex: #42 (Hint: Recall the cross-product will result in a vector that is orthogonal to both gradients and thus tangent to both surfaces! !) ‘ Z‘Xzfyl ; 3:4-y @z,r:,s‘) \\ FCW/% X915“? (,7 : Li — y - z Yz—l 4'th \l. ‘ __— 2:5’44: k6 l/L’ZJ l< ’5"])¢ 35"“? Elm l ‘1 l: X Mm _._. JLG5V thvG] ‘ J K E Kbﬁ 6: m“ L, —2 'I = (L JleJ ”41k ‘0 Thu-b Law lVr- . ,ﬂ ch 0—. w m PM no N ...
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