Magnitude of Vector Question?

Question

I found the component form of the vector but can't seem to figure out the magnitude of the vector. Appreciate it if I can get some help

Suppose u=<8, -4> and v=<-1,7>. Find the magnitude of the vector 2u-2v.

Here is the component form that I already figured out:

<18, -22>

Answer 1

The magnitude of &lt;x, y&gt; = √x² + y²

(Both the x² + y²  are under the square root)

So, 2u - 2v = 2&lt;8,-4&gt; - 2&lt;-1, 7&gt;

= &lt;16+2, -8-14&gt; = &lt;18, -22&gt;

Good job. Now, to find the magnitude, we say

||L|| = √18² + (-22)²  = √324+484 = 28.43

The magnitude of 2u-2v = 28.43

Answer 2

If you have a vector V = &lt;x, y&gt; then its magnitude is always sqrt(x² + y²).

In your case, the answer is sqrt(324 + 444) = sqrt(808) = 2sqrt(202).