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question #2 reference q.46912 \thinking cap!\: vectors and trigonometry seem to work in a 2 - dimensional world. can they be used to navigate in 3 dimensions or on the surface of the world which is spherical?
Vectors and trigonometry can be extended to 3 - D and spherical surfaces. In 3 - D, vector operations like addition, subtraction, and dot - cross products are well - defined. For spherical surfaces, spherical trigonometry is used to solve problems related to navigation, astronomy etc.
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Yes, vectors and trigonometry can be used to navigate in 3 dimensions and on the spherical surface of the world.