Vector Finding Challenge

Find three vectors which have the following properties. Let me know how you did it.

1) All three vectors are 3D (three-dimensional)
2) All three vectors have the same length
3) All three vectors are mutually orthogonal (perpendicular)
4) All three vectors are composed solely of integers (positive or negative)

#Geometry

Easy Math Editor

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Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

I'm only proposing a process at this stage. Can't you just cook up a set of three vectors then use the Gram-Schmidt process to orthonormalise them, all the while hope for the best? Sure, some trial and error may be involved, but it doesn't seem like something that's not doable. I just choose to invest my time elsewhere, where the pastures are greener.

A Former Brilliant Member - 2 years, 8 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$