`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

`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((20i+25j)*(20i+25j))=`

`=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...

`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(20^2+(25)^2)`

`sqrt1025`
`32.0` is the magnitude

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