Find if possible an orthogonal unit vector at: 2i + 3j  k and  2i  3j + 4k
1,061
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. $$Pv=\frac{xx^T}{x^2}v$$
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MA
Updated on June 17, 2022Comments

MA 11 months
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 $\dfrac{[ 9, 6, 0 ]}{\sqrt{117}}.$

TMM over 10 yearsI assume you are using the cross product to obtain $(9, 6, 0)$ which is orthogonal to $(2, 3, 1)$ and $(2, 3, 4)$. In that case, what you did is correct.

Mark Bennet over 10 yearsI think you are having problems expressing yourself in a form which will enable you to get help from this forum. You seem to have applied a method which will work, but you haven't asked us a question  are you unsure why this works? Or are you unsure of the method and want to confirm it before tackling some other similar problems? Or .. it is unclear what you want to achieve.

Lemon over 10 years"orthogonal unit vector", also known as orthonormal
