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klio [65]
3 years ago
14

The vector has components +5 and +7 along the x- and y-axes respectively. along a set of axes rotated 90 degrees counterclockwis

e relative to the original axes, the vector's components are

Mathematics
2 answers:
Natali5045456 [20]3 years ago
8 0
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.
lisabon 2012 [21]3 years ago
6 0
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)

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