Problem 1 (15 points) Find a vector \(\vec{D} = D_x\hat{a}_x + D_y\hat{a}_y + D_z\hat{a}_z\) that satisfies the following conditions: \begin{cases} \vec{D} \cdot \hat{a}_x = 0\\ \vec{D} \cdot \hat{a}_\phi = 0 \quad at \ (\rho = 1, \phi = 45^\circ, z = 1) \\ \vec{D} \cdot (2\hat{a}_x + 4\hat{a}_y - 2\hat{a}_z) = -6 \end{cases}
Added by Andrea T.
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Step 1
a] = 0, which means that the dot product of vector D and vector a is equal to zero. This can be written as Da * 1 + Db * 0 + Dc * 0 = 0. Simplifying this equation, we get Da = 0. Show more…
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