(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

given z = (0, 0, 0, 1), and v = (0, x, y, z),

and the following properties hold

[tex] v \times u = L [/tex]

[tex] L \times v = u [/tex]

[tex] u \times L = v [/tex]

v, u, l, and z are unit quaternions

In other words; we define forward (v), up (u) and right(L), find a unit quaternion that when you apply it on z, you get v, in the proper orientation.

solve for q = (a, b, c, d)

2. Relevant equations

(equation to solve for q)

[tex]qzq^{-1} = v[/tex]

Left side applys q on z and right side is v

3. The attempt at a solution

[tex] qz = vq [/tex]

[tex] dk = (xi + yj + zk)(a + bi + cj + dk) [/tex]

after expanding and grouping the terms on the same axis together. In a matrix form I got

[tex] \left(

\begin{array}{cccc}

x & y & z & 0 \\

0 & z & y & x \\

z & 0 & -x & y \\

-y & x & -1 & z

\end{array}

\right)

\left(

\begin{array}{c}

a \\

b \\

c \\

d

\end{array}

\right)

=

\left(

\begin{array} {c}

0 \\

0 \\

0 \\

0

\end{array}

\right)

[/tex]

[a, b, c, d] = [0, 0, 0, 0] ? That doesn't seem right?

Shouldn't I need to use atleast the vector u?

Thank you for your help

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# Ax = b when b = [0; 0; 0; 0]

Can you offer guidance or do you also need help?

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