`u = 12i - 16j` Use the dot product to find the magnitude of u.

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 `i` and `j` are orthonormal. Therefore

 `||u||=sqrt(u*u)=sqrt((12i-16j)*(12i-16j))=`

`=sqrt(12*12+(-16)*(-16))=4sqrt(3*3+4*4)=4sqrt(25)=20.`

This is the answer.

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 `i` and `j` are orthonormal. Therefore

 `||u||=sqrt(u*u)=sqrt((12i-16j)*(12i-16j))=`

`=sqrt(12*12+(-16)*(-16))=4sqrt(3*3+4*4)=4sqrt(25)=20.`

This is the answer.