Magnitude of <2, 3, 6>

Step by step

The question

Question: find the length of v = ⟨2, 3, 6⟩.

1 Draw it

Draw the three axes.

The arrow starts at the origin.

Go 2 along x, 3 along y, 6 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.

2 squared is 4.

3 squared is 9.

6 squared is 36.

Add: 4 plus 9 plus 36 is 49.

7 times 7 is 49.

So ‖v‖ = 7.

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 13.

Then up z: 13 plus 36 is 49.

The same!

Let's look back.

First: draw it.

Then: find the length.

Last: check.