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by: Andrew Swann

140

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# MultiVariable Calculus Three

Marketplace > MultiVariable Calculus Three
Andrew Swann
GWU
GPA 2.14

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COURSE
PROF.
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TYPE
Bundle
PAGES
2
WORDS
KARMA
75 ?

## Popular in Department

This 2 page Bundle was uploaded by Andrew Swann on Friday January 30, 2015. The Bundle belongs to a course at a university taught by a professor in Fall. Since its upload, it has received 140 views.

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Date Created: 01/30/15
Vectors Vectors nothing new 0 Add vectors part by part 0 Multiply by distribution Dot Products 0 Properties all quotXquot are dots UXvVXu Cu X V cv X u UXvwuXvuXw U X u uA2 Use dot at all times 0 Corollaries Used to test if perp bc the cos 90 would make right side 0 perp orthogonal normal 0 Law of cosines v uIA2 uA2 IVIAZ 2uvcos 9 0 Results in the equation highlighted when simpli ed Cauchy Schwarz Inequality O U X V lt uv 0 quotV componentquot of u just like X component in physics ucos u X v v 0 Cross product actually uses quotXquot not dots 0 If u ltabcgt amp ltdefgt then u X V ltbfce cd af ae bdgt 0 Only works in the third dimension unlike dot product 0 Always goes in the direction that is normal to both u and V as long as u and V are NOT parallel Cross Products 00000 0 Cross products U X V V X u Cu X V cu X V U dot V X w u X V dot w volume of cube made by uvw UXVXwntuXVXw U dot V X w is solved by a determinant of a matriX u X VI uv sing area of the parallelogram Divide by two if you want the triangle in 3d 0 Planes amp Lines 0 V ltabcgt vector orthogonal to the plane p de f Xyz on the plane or notmust check to see if it forms a 90degree angle Use X d y e Z f dot abc 0 if it forms a 90 aX d by e cz f Where every plane will have some form of this equation Eg 5X 3y 8Z 13 where lt5 3 8gt is the vector and some form of ltabcgt is the point If the new vector is parallel then it is on the plane aka the new vector is some variable of ltabcgt or ltX d y e Z fgt ltabcgt OOOOOO 0 If no z then it39s vertically oriented Vector Valued Functions Usually represented by rt instead of fX 0 Where rt might ltXtytztgt 0 But the function is the arrow from the origin to the point

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