Question

Please help ASAP!!!! The magnitude and direction of the two vectors are shown in the diagram. What is the magnitude of their sum?

Answer 1

`2√(5)`

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:

`h^2 = c_1^2 + c_2^2`

Let's plug in the known values (the length of the vectors) and solve this

`h^2 = 2^2 + 4^2\\h^2 = 20 \\h = √(20)\\h = √(2\cdot 2\cdot 5)\\h = √(2^2 \cdot 5)\\h = 2√(5)\\`

Good luck!