(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

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Ax = b when b = [0; 0; 0; 0]

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**