"If all the components of a vector are equal to 1, then that vector is a unit vector." Is this true or false?
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Tushar Chandra
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A unit vector is basically a vector meant to specify a direction. It has a length of 1.
For any vector `veca` , the corresponding unit vector is `hata = veca/||a||` . This has the same direction as that of `veca` but a magnitude equal to 1.
If all the components of a vector are equal to 1, the magnitude of the vector is `sqrt(1^1 +1^1 +1^1)` = `sqrt 3` . This is not a unit vector.
The statement "If all the components of a vector are equal to 1, then that vector is a unit vector." is false.
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