MAT 201 - Review Session 1

MAT 201 - Review Session 1 - Math Review#1 with Adrian...

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Math Review #1 with Adrian Banner September 18, 2007 VECTORS -Vectors have both direction and length. -They can be represented by many different notations: -an arrow written above the symbol, pointing to the right -an underline -a squiggle thing underneath -boldface -The length of a vector is represented by | V |. -If V = (v 1 , v 2 ), then | V| = sqrt(v 1 2 + v 2 2 ) -e.g. |(3,2)| = sqrt(3 2 + 2 2 ) = sqrt(13). -To add vectors, place them tip to tail (arrow part to non-arrow part). -Draw the resultant from tip of first vector to tail of second vector. -This is the same as the parallelogram (resultant is diagonal of parallelogram). -To subtract vectors, you need scalar multiplication. -A scalar is simply a length without a direction. -Given vector V and positive scalar λ . - λ V is a vector pointing in the same direction as V but λ times as long. -If λ is negative, λ V points in the opposite direction of V . -If λ is zero, you get the zero vector, which has no length or direction. -Thus to subtract vectors, simply add a negative vector, U - V = U + (- V ), then do the same thing as addition. -Unit vectors have length one. -If V is a vector, then V /| V | is a unit vector pointing in the same direction. -e.g. Given V = (3,2) -| V | = sqrt(13) -1/sqrt(13) * V = (3/sqrt(13), 2/sqrt(13)) is a unit vector - i and j are unit vectors along the unit axes. - V = (3,2) is actually a shorthand -The proper way to write it is 3 i + 2 j -Multiplication of two vectors: the dot product! -Given two numbers x, y, x y = ½(x 2 + y 2 – (x – y) 2 ) -Dot product: u v = ½(| u | 2 + | v | 2 - | u - v | 2 ) - There’s an easier way to do it. -Draw the triangle for
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This note was uploaded on 02/28/2009 for the course MAT 201 taught by Professor Thomaschen during the Fall '07 term at Princeton.

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MAT 201 - Review Session 1 - Math Review#1 with Adrian...

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