Multivariable Calculus parameter equation of line tangent to a point in vector space

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Find parameter equations of the line tangent to the helix C: Vector_r = Vector_icos(t) + Vector_jsin(t) + tVector_k at the point P(-1, 0, Pi) where t = Pi.
The solution on the book is Vector_r(Pi) + tVector_r'(Pi). And I don't understand why there is a Vector_r involved here.
Source: Multivariable Calculus by C. Henry Edward's, David E. Penney, page 806

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