Lab 2 Notes.pdf - MA122 Lab Report 2 Notes Vectors in Rn 1 When n = 2 x T where(x y can be thought of as the point on the xy-axes(i.e two dimensional =

Lab 2 Notes.pdf - MA122 Lab Report 2 Notes Vectors in Rn 1...

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MA122 Lab Report 2 Notes Vectors in R n : 1. When n = 2 : Denoted by °! a = a = ° x y ± = ² x y ³ T where ( x; y ) can be thought of as the point on the xy -axes (i.e. two dimensional) and the vector is an arrow from the origin to the point. 2. When n = 3 : Denoted by °! a = a = 2 4 x y z 3 5 = x °! i + y °! j + z °! k where ( x; y; z ) can be thought of as the point on the xyz -axes (i.e. three dimensional) and the vector is an arrow from the origin to the point. Note: °! i = 2 4 1 0 0 3 5 , °! j = 2 4 0 1 0 3 5 ; and °! k = 2 4 0 0 1 3 5 are called the standard basis for R 3 : 3. When n > 3 : Denoted by °! a = 2 6 6 6 4 x 1 x 2 . . . x n 3 7 7 7 5 which can no longer be visualized but is still an arrow from the origin to a "point". Vector Calculations: Given °! a = a = ² x 1 x 2 ± ± ± x n ³ T , °! b = b = ² y 1 y 2 ± ± ± y n ³ T ; and k 2 R ; the following properties hold when n = 2 ; 3 ; ::: : 1. Addition: ~a + ~ b = ² x 1 ± ± ± x n ³ T + ² y 1 ± ± ± y n ³ T = ² x 1 + y 1 ± ± ± x n + y n ³ T Geometrically, it you draw a parallelogram with ~a and ~ b being adjacent sides, then ~a + ~ b is the vector from the origin to the vertex of the parallelogramopposite the origin.
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