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The question is:

Find, if possible, an orthogonal unit vector at: $2i + 3j - k$ and $-2i - 3j + 4k$.

$\left|\begin{matrix} i & j & k \\ 2 & 3 & -1 \\ -2 & -3 & 4 \end{matrix}\right| = [9, -6, 0]$

His norm is $\sqrt{117}$

The orthogonal unit vector is $\dfrac{[ 9, -6, 0 ]}{\sqrt{117}}.$

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    "orthogo$n$al unit vector", also known as orthonormal2012-11-02

1 Answers 1

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Your question needs to be more detailed and organized because I am not exactly sure what you want? If you are wanting to know how to get orthonormal vectors then you can use projections. The projection onto a vector x is give by. $Pv=\frac{xx^T}{||x||^2}v$