Determine the components of this resultant with respect to N and T axes rotated 30 deg counterclockwise
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Determine the components of this resultant with respect to N and T axes rotated 30 deg counterclockwise
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[tex]\LARGE\tt✏ MATHEMATICS :[/tex]
To determine the components of a resultant vector with respect to N (north) and T (east) axes rotated counterclockwise by 30 degrees, we need to consider the original components of the vector and rotate them accordingly.
Let's assume the original components of the resultant vector are Rx and Ry with respect to the original x and y axes, respectively.
To find the components with respect to the rotated N and T axes, we need to rotate the original components counterclockwise by 30 degrees. This rotation can be achieved using the following rotation matrix:
[R_n] [cosθ -sinθ] [Rx]
[R_t] = [sinθ cosθ] × [Ry]
Where θ is the rotation angle, in this case, 30 degrees.
Substituting the values:
[R_n] [√3/2 -1/2] [Rx]
[R_t] = [1/2 √3/2] × [Ry]
Let's calculate the components:
[R_n] = (√3/2) × Rx + (-1/2) × Ry
[R_t] = (1/2) × Rx + (√3/2) × Ry
These components [R_n] and [R_t] represent the resultant vector components with respect to the rotated N and T axes, respectively, after a counterclockwise rotation of 30 degrees.
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