`u = 20i + 25j` 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


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


I suppose that `i` and `j` are orthonormal. Therefore



`=sqrt(20*20+25*25)=5sqrt(4*4+5*5)=5sqrt(41) approx 32.`

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.


`32.0` is the magnitude