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

Original Vector components are + 5 in x-axis & + 7 in y-axis,

After rotating 90 degrees counterclockwise,

Now, Vector components are + 7 in x-axis & + 5 in y-axis.

Refer to the diagram shown below.

Let the coordinates of the rotated vector be (a, b).

From the Pythagorean theorem,

d = √ (5² + 7²) = 8.6023

The angle θ is given by

tan θ = 7/5 = 1.4

θ = tan⁻¹ 1.4 = 54.46°

φ = 180 - (90 + 54.46) = 35.54°

The coordinates of the rotated vector are

a = - d cos φ = - 8.6023*cos (35.54) = 7

b = d sin φ = 8.6023*sin (35.54) = 5

Answer: (-7, 5)