`u = -21i` Use the dot product to find the magnitude of u.

Expert Answers
Borys Shumyatskiy eNotes educator| Certified Educator

The magnitude of a vector `u` is the square root of its dot product by itself, because

`u*u=||u||*||u||*cos(theta),` and `theta=0,` `cos(theta)=1.`


I suppose that the magnitude of `i` is 1. Then

`||u||=sqrt(u*u)=sqrt((-21i)*(-21i))=sqrt(21*21)=21.`

This is the answer.

loves2learn | Student

There's no way to have a dot product, because there is only one vector. A dot product is two vectors multiplied together.

Using the Pythagorean theorem...

`a^2+b^2=c^2`

where a is the x coordinate, b is the y coordinate, and c is the length of the vector.

`sqrt(a^2+b^2)=c`
after taking the square root of both sides.

`sqrt((-21)^2)`

`sqrt441`
`21 ` is the magnitude

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