Question

Convert to proper fraction or mixed number (do not reduce to lowest terms)
.8

Answer 1

8/10

Answer 2

thank u

Answer 3

\[k = (k _{1},k _{2},k _{3})\]

Answer 4

\[k_{1} = U_{x}\]
\[k_{2} = U_{y}\]
\[k_{3} = U_{z}\]

derive x value of the middle line in the rotation matrix using:
\[V[0], k[0], (k ^{\tau} V), ([k]\times V)[0]\]

\[(0)\cos \theta + (-U_z)\sin \theta + (U_x)(U_y)(1- \cos \theta)\]
\[= U_{x}U_{y}(1-\cos \theta) - U_{z}\sin \theta\]

derive y value of the middle line in the rotation matrix using:
\[V[1], k[1], (k ^{\tau} V), ([k]\times V)[1]\]

\[(1)\cos \theta + (0)\sin \theta + (U_y)(U_y)(1- \cos \theta)\]
\[= \cos \theta + U_{y}^2(1-\cos \theta)\]

derive z value of the middle line in the rotation matrix using:
\[V[2], k[2], (k ^{\tau} V), ([k]\times V)[2]\]

\[(0)\cos \theta + (U_x)\sin \theta + (U_z)(U_y)(1- \cos \theta)\]
\[= U_{z}U_{y}(1-\cos \theta) + U_{x}\sin \theta\]