A rotated set of basis vectors \(\hat{u}\), \(\hat{v}\) is shown below relative to the Cartesian basis \(\hat{i}\), \(\hat{j}\). The rotation angle is \(\theta = 70^\circ\) as shown. Matlab/Mathematica input: theta = 70; What are \(\hat{u}\), \(\hat{v}\) in terms of \(\hat{i}\), \(\hat{j}\)? \(\hat{u} = \underline{\qquad}\hat{i} + \underline{\qquad}\hat{j} \(\hat{v} = \underline{\qquad}\hat{i} + \underline{\qquad}\hat{j}
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First, we need to find the components of the rotated basis vectors &i and U in terms of the original basis vectors i and j. We can use the rotation matrix for counterclockwise rotation by an angle of theta: R = [cos(theta) -sin(theta); sin(theta) cos(theta)] In Show more…
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