`u = <-8, 15>` 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 product by itself, because

`u*u=||u||*||u||*cos(theta),`


and `theta=0,` `cos(theta)=1.` So

 

`||u||=sqrt(u*u)=sqrt(lt-8,15gt*lt-8,15gt)=`
`=sqrt((-8)*(-8)+15*15)=sqrt(64+225)=sqrt(289)=17.`

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((-8)^2 + (15)²) `
`sqrt(64 + 225) `
`sqrt(289) `
 17 is the magnitude

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