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

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)

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.