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Question

Can a vector have zero component along a line and still have nonzero magnitude?

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Solution

Yes, a vector can have zero components along a line and still have a nonzero magnitude.
Example: Consider a two dimensional vector 2i^+0j^. This vector has zero components along a line lying along the Y-axis and a nonzero component along the X-axis. The magnitude of the vector is also nonzero.
Now, magnitude of 2i^+0j^ = 22+02=2

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