Math Questions and Answers

Start Your Free Trial

"If all the components of a vector are equal to 1, then that vector is a unit vector." Is this true or false?

Expert Answers info

Tushar Chandra eNotes educator | Certified Educator

calendarEducator since 2010

write12,554 answers

starTop subjects are Math, Science, and Business

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.

check Approved by eNotes Editorial