A vector vec{a} = 2hat{i} + 3hat{j} + 7hat{k} | vedclass

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(D) Let the original unit vectors be $\hat{i}, \hat{j}, \hat{k}$. When the coordinate system is rotated by $\pi / 2$ about the $z-$axis such that the

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$(3, -2, 7)$

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(D) Let the original unit vectors be $\hat{i}, \hat{j}, \hat{k}$. When the coordinate system is rotated by $\pi / 2$ about the $z-$axis such that the $x-$axis moves to the $y-$axis,the new unit vectors $\hat{i}'$ and $\hat{j}'$ are related to the old ones as follows:$\hat{i}' = \hat{j}$$\hat{j}' = -\hat{i}$$\hat{k}' = \hat{k}$Given $\vec{a} = 2\hat{i} + 3\hat{j} + 7\hat{k}$.We can express $\hat{i} = -\hat{j}'$ and $\hat{j} = \hat{i}'$.Substituting these into the expression for $\vec{a}$:$\vec{a} = 2(-\hat{j}') + 3(\hat{i}') + 7\hat{k}'$$\vec{a} = 3\hat{i}' - 2\hat{j}' + 7\hat{k}'$Thus,the new components are $(3, -2, 7)$.

$A$ vector $\vec{a} = 2\hat{i} + 3\hat{j} + 7\hat{k}$ is given in a right-handed rectangular coordinate system. If the coordinate system is rotated about the $z-$axis from the positive $x-$axis to the positive $y-$axis through an angle of $\pi / 2$,then the new components of $\vec{a}$ will be:

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