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04Magnitude of a Vector and Unit Vectors

04Magnitude of a Vector and Unit Vectors - If we are given...

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D ISTANCE B ETWEEN P OINTS , M AGNITUDE OF A V ECTOR , AND U NIT V ECTORS To find the distance between two points, use the distance formula: 2 1 2 2 1 2 ) ( ) ( y y x x d - + - = - for two dimensions 2 1 2 2 1 2 2 1 2 ) ( ) ( ) ( z z y y x x d - + - + - = - for three dimensions Ex . Find the distance between the points (-1, 4) and (-6, 11). Ex . Find the distance between the points (3, -1, 4) and (4, 7, -2). The length of a vector is the magnitude of the vector or its absolute value . The length of a vector a is represented by 2 2 2 1 2 1 a a a a a + = = . Ex . Find the length of the vector j i b 7 2 - = .

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Ex . Find p if - - = 1 4 3 p . A unit vector is any vector which is one unit long. The length of a vector is used to calculate
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Unformatted text preview: If we are given a vector a , the unit vector a ˆ , is a vector of length one unit in the same direction as a . To change the length of the vector to one, divide the original vector by its length. a a a = ˆ Ex . Given j i q 2 5-= , find its unit vector. You could also write it in column representation: Ex . Find unit vectors in the same direction as each vector. a) -4 6 3 b) -2 1 2 4 Assign: MM p.239 Exercise 13.3 #1-3, MSL p.370 Exercise 15G #1-6...
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