Magnitude for Items in Boxes

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Kris Caballero • Jun 30, 2026 • 0 comments • Linear Algebra

$CaballeroMath Linear Algebra #1: Part A - You received a package of shipping boxes for your online store. The largest box you have measures 9 x 15 x 11 feet. How long an item will you able to fit into that very box, diagonally?$

$CaballeroMath Linear Algebra #1: Part B - You received a package of shipping boxes for your online store. The largest box you have measures 9 x 15 x 11 feet. How long an item will you able to fit into that very box, diagonally?$

$CaballeroMath Linear Algebra #1: Part C - You received a package of shipping boxes for your online store. The largest box you have measures 9 x 15 x 11 feet. How long an item will you able to fit into that very box, diagonally?$

$CaballeroMath Linear Algebra #1: Part D - You received a package of shipping boxes for your online store. The largest box you have measures 9 x 15 x 11 feet. How long an item will you able to fit into that very box, diagonally?$

$CaballeroMath Linear Algebra #1: Part E - You received a package of shipping boxes for your online store. The largest box you have measures 9 x 15 x 11 feet. How long an item will you able to fit into that very box, diagonally?$

$CaballeroMath Linear Algebra #1: Part F - You received a package of shipping boxes for your online store. The largest box you have measures 9 x 15 x 11 feet. How long an item will you able to fit into that very box, diagonally?$

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You received a package of shipping boxes for your online store. The largest box you have measures 9 x 15 x 11 feet. How long an item will you able to fit into that very box, diagonally?

The largest box we received is 9 x 15 x 11 feet; we can use these numbers in the form of a vector. A vector is a directional property—an arrow—that has length and magnitude.

Let $\textbf{b}$ represent the vector in which our box's numerical elements hold. Because this is in writing, whereas vectors in typing are boldfaced, we place an arrow above our variable. Thus,

$\vec{b}$

Write our vector's elements as

$\vec{b} = \begin{bmatrix} 9 \\ 15 \\ 11 \end{bmatrix}$

Having to fit an item into this box requires calculating its length. In other words, we need to find our vector's magnitude.

Let $\vec{b}$ be the magnitude of our vector to find its length. Thus,

$${ \lVert b \rVert }$$

Where

$${ \lVert b \rVert = \sqrt{v_1^2 + v_2^2 \ldots + v_n^2}}$$

and $v_1, v_2, \ldots v_n$ represent our vector's elements.

Plug in our vector's elements for calculation and we get

$${ \lVert b \rVert = \sqrt{9^2 + 15^2 + 11^2}}$$

Exponentiate first, then add all elements:

$${ \lVert b \rVert = \sqrt{81 + 225 + 121}}$$

$${ \lVert b \rVert = \sqrt{427}}$$

Take its square root (round, if necessary):

$${ \lVert b \rVert = \sqrt{427} \approx 20.66 \ \ or \ \ 20.7 feet}$$

Therefore, the largest item you can fit in a shipping box that measures 9 x 15 x 11 feet is 20.7 feet.

We hope you learned something new! Feel free to contact us, if you have any questions or would like to add to this article teaching about the terms we've discussed here!

(NOTE: This marks as our very first, official tutorial post here on KCU Network of Mathematics!)
(UPDATE [July 05, 2026 @ 3:31pm PST]: Edited LaTeX syntax.)

Credits and a thank you to MathJax for this beautiful LaTeX library!

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$Kris Caballero - founder and CEO of KC Universal Network$

Kris Caballero

Founder of KCU Network and KCU Plus, Kris has been writing since he managed a personal blog back in late 2005. Officially back to doing computer programming (software development), Kris enjoys reading books on Mathematics, Quantum Computing, Philosophy, playing old video/DOS games, digital video archiving, and listening to sports, public radio and classical music.