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Definition of Vector Component
A vector component is a projection of a vector onto the horizontal or vertical axis.
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Don't be fooled by this question; there is nothing to be fooled by. A vector directed northwest has components that are directed north and west. The northern component is the projection of the vector onto the north-south axis. The western component is the projection of the vector onto the east-west axis. A vector directed southeast has components which are directed south and east. The southern component is the projection of the vector onto the north-south axis. The eastern component is the projection of the vector onto the east-west axis.
So to answer this question, simply look at the given vector and ask In which two directions is this vector pointing? The answer to your question is the answer you should pick.
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Mathematically, a component is simply a projection of a vector onto an axis. To determine the components using a diagram, first draw the vector. Then sketch the x-y coordinate axes at the tail of the vector. From the arrowhead of the vector, sketch reference lines across to each of the coordinate axes such that the lines meet the axes with a perpendicular orientation to them. The x-component stretches along the x-axis from the tail of the vector to the location where the reference line meets the x-axis. The y-component stretches along the y-axis from the tail of the vector to the location where the reference line meets the y-axis.
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