`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


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...


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

after taking the square root of both sides.


`21 ` is the magnitude