Question: expressing the vector A = 3i + 2j + kin terms of triad i'j'k'' where...

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Question: expressing the vector A = 3i + 2j + kin terms of triad i'j'k'' where the x y - axis are rotated 45 around the Z-axis , with z and z-axis coinciding, as shown in figure below > referring to the figure, we have for the coefficients of transformation i. i = cos 45 and so on: hence Li=112 i.f=-12 j.i = 1/2 1.5=12 k.i = 0 k. j = = 0 i.k = 0 j.k' = 0 k. k = 1 == 22' 45 These gives 3 2 Ax = = 2 2 5 So that, in the primed system, the vector A is given by i- 1 A = = j + k 1.9 Derivative of a Vector Ay -3 2 ts 45 A = 1 H.W Question: expressing the vector A = 3i + 2j + kin terms of triad i'j'k'' where the x y - axis are rotated 45 around the Z-axis , with z and z-axis coinciding, as shown in figure below > referring to the figure, we have for the coefficients of transformation i. i = cos 45 and so on: hence Li=112 i.f=-12 j.i = 1/2 1.5=12 k.i = 0 k. j = = 0 i.k = 0 j.k' = 0 k. k = 1 == 22' 45 These gives 3 2 Ax = = 2 2 5 So that, in the primed system, the vector A is given by i- 1 A = = j + k 1.9 Derivative of a Vector Ay -3 2 ts 45 A = 1 H.W