Test1_formulas_sp10

Test1_formulas_sp10 - VECTORS, LINES, PLANES Vector:...

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VECTORS, LINES, PLANES Vector: collection of arrows with common length and direction - notations: a = h a 1 ,a 2 ,a 3 i = a 1 i + a 2 j + a 3 k - magnitude (length): | a | = p a 2 1 + a 2 2 + a 2 3 - Unit vector in the direction of a : u = a | a | - vector between the points P 0 ( x 0 ,y 0 ,z 0 ) and P 1 ( x 1 ,y 1 ,z 1 ): ---→ P 0 P 1 = h x 1 - x 0 ,y 1 - y 0 ,z 1 - z 0 i . Dot product - Definitions: . h a 1 ,a 2 ,a 3 i · h b 1 ,b 2 ,b 3 i = a 1 b 1 + a 2 b 2 + a 3 b 3 . a · b = | a || b | cos θ ( θ is the angle between a and b ) - Scalar projection of b onto a : a · b | a | - Vector projection of b onto a : a · b | a | 2 a - The length of the vector projection is the absolute value of the scalar projection - Perpendicular: a b if and only if a · b = 0 Cross Product - Definition: h a 1 ,a 2 ,a 3 i × h b 1 ,b 2 ,b 3 i = i j k a 1 a 2 a 3 b 1 b 2 b 3 - Properties: . | a × b | = | a || b | sin θ . a × b is perpendicular to both a and b . ( a , b , a × b
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Test1_formulas_sp10 - VECTORS, LINES, PLANES Vector:...

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