Question

1) Consider a vector $\vec{A}$ in two different rectangular coordinate systems, one primed and the other unprimed. The primed coordinate system is rotated counterclockwise through an angle $\theta$, with respect to the unprimed coordinate system. The vector $\vec{A}$ is fixed during this rotation about the z-axis. Find the relationship between the components of $\vec{A}$ in the primed system, expressing the primed components in terms of the unprimed components. (i) Draw the figure for the rotation of the primed coordinate system with respect to the unprimed coordinate system. $\vec{A}$ is fixed during this rotation. (ii) Use this figure to find: $A'_x = ?$ $A'_y = ?$ 2) Show that the length of $\vec{A}$ is the same in the primed and unprimed frames: $||\vec{A}|| = \sqrt{(A'_x)^2 + (A'_y)^2} = \sqrt{(A_x)^2 + (A_y)^2}$

          1) Consider a vector $\vec{A}$ in two different rectangular coordinate systems, one primed and the other unprimed. The primed coordinate system is rotated counterclockwise through an angle $\theta$, with respect to the unprimed coordinate system. The vector $\vec{A}$ is fixed during this rotation about the z-axis. Find the relationship between the components of $\vec{A}$ in the primed system, expressing the primed components in terms of the unprimed components. (i) Draw the figure for the rotation of the primed coordinate system with respect to the unprimed coordinate system. $\vec{A}$ is fixed during this rotation. (ii) Use this figure to find:
$A'_x = ?$
$A'_y = ?$
2) Show that the length of $\vec{A}$ is the same in the primed and unprimed frames: $||\vec{A}|| = \sqrt{(A'_x)^2 + (A'_y)^2} = \sqrt{(A_x)^2 + (A_y)^2}$

1 consider a vector veca in two different rectangular coordinate systems one primed and the other unprimed the primed coordinate system is rotated counterclockwise through an angle theta wit 70628

Added by Marcos B.

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