The vector `vecA` has components + 5 and + 7 along the x-axes and y-axes, respectively. Along a set of axes rotated 90 degrees counterclockwise relative to the original axes, the vector's components are

Options

A. `-7,-5`
B. `7,-5`
C. `-7,5`
D. `7,5`

Answer

To solve the problem, we need to determine the components of the vector \(\vec{A}\) after the coordinate axes have been rotated 90 degrees counterclockwise. The original components of the vector are given as:

- \(A_x = +5\) (along the x-axis)
- \(A_y = +7\) (along the y-axis)

### Step 1: Understand the Rotation of Axes
When we rotate the axes 90 degrees counterclockwise, the new axes \(x'\) and \(y'\) will be oriented as follows:
- The original positive x-axis will now point in the direction of the positive y-axis.
- The original positive y-axis will now point in the direction of the negative x-axis.

### Step 2: Determine the New Components
To find the new components of the vector \(\vec{A}\) in the rotated coordinate system:
- The new x-component \(A_{x'}\) will be equal to the original y-component \(A_y\).
- The new y-component \(A_{y'}\) will be equal to the negative of the original x-component \(A_x\).

Thus, we can express this mathematically as:
- \(A_{x'} = A_y = +7\)
- \(A_{y'} = -A_x = -5\)

### Step 3: Write the Final Answer
After performing the calculations, we find that the components of the vector \(\vec{A}\) along the new axes are:
- \(A_{x'} = +7\)
- \(A_{y'} = -5\)

Therefore, the components of the vector \(\vec{A}\) along the rotated axes are:
\[ \vec{A} = (7, -5) \]

### Conclusion
The correct answer is \(A_{x'} = +7\) and \(A_{y'} = -5\).

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