Magnitude of <4, 4, 7>

Step by step

The question

Question: find the length of v = ⟨4, 4, 7⟩.

1 Draw it

Draw the three axes.

The arrow starts at the origin.

Go 4 along x, 4 along y, 7 along z.

The arrow goes from the origin to the end of that path.

2 Find the length

The length ‖v‖ is Pythagoras with three parts.

Square each part, add, then take the square root.

4 squared is 16.

4 squared is 16.

7 squared is 49.

Add: 16 plus 16 plus 49 is 81.

9 times 9 is 81.

So ‖v‖ = 9.

Careful!

We don't add the parts.

The arrow is the long side of a right triangle, so we square, add, and take the root.

3 Check

Let's check it as Pythagoras twice.

Across the floor the square is 32.

Then up z: 32 plus 49 is 81.

The same!

Let's look back.

First: draw it.

Then: find the length.

Last: check.