Question

Can a vector have nonzero magnitude if a component is zero? if no, why not? if yes, give an example.

Answer 1

Can a vector have nonzero magnitude if a component is zero?

Yes, a vector can have zero components along a line and still have a non-zero magnitude.

Example: Consider a two dimensional vector 2i + 0j. This vector has zero components along a line lying along the Y - axis and a non- zero component along the X - axis. The magnitude of the vector is also non - zero.

Now, magnitude of 2i + 0j = $\sqrt2^2+\sqrt0^2$=2

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