Answer:
[tex]2\sqrt{5}[/tex]
Step-by-step explanation:
To add these vectors together, we have to "glue" them together.
Let's call the vector with the length of 2 A and the one with length 4 B.
Imagine you can grab vector A with your hands and move it to the end of B (it would look like the image that's annexed)
Now imagine that we made a triangle from that, what we want to know is the hypotenuse of that triangle!
We know that when we want to find the hypotenuse of a triangle, we can use Pythagoras theorem:
[tex]h^2 = c_1^2 + c_2^2[/tex]
Let's plug in the known values (the length of the vectors) and solve this
[tex]h^2 = 2^2 + 4^2\\h^2 = 20 \\h = \sqrt{20}\\h = \sqrt{2\cdot 2\cdot 5}\\h = \sqrt{2^2 \cdot 5}\\h = 2\sqrt{5}\\[/tex]
Good luck!
