Answers:

(i)

R(1, -3, 4) and S(4, -2, -3)

(x₁,y₁,z₁) = (1, -3, 4)

(x₂,y₂,z₂) = (4, -2, -3)

$\begin{array}{l}

D = \sqrt {{{({x_2} – {x_1})}^2} + {{({y_2} – {y_1})}^2} + {{({z_2} – {z_1})}^2}} \\

D = \sqrt {{{( 4 – 1)}^2} + {{(-2-(-3))}^2} + {{( – 3-4)}^2}} \\

D = \sqrt {9 + 1 + 49} \\

D = \sqrt {59}

\end{array}$

Distance between points R and S is √59 units.

(ii)

C(9, -12, -8) and the origin Coordinates of origin are (0, 0, 0)

(x₁,y₁,z₁) = (9, -12, -8)

(x₂,y₂,z₂) = (0, 0, 0)

$\begin{array}{l}

D = \sqrt {{{({x_2} – {x_1})}^2} + {{({y_2} – {y_1})}^2} + {{({z_2} – {z_1})}^2}} \\

D = \sqrt {{{( 0 – 9)}^2} + {{(0 – (-12))}^2} + {{( 0 – (-8))}^2}} \\

D = \sqrt {81 + 144 + 64} \\

D = \sqrt {289}

\end{array}$

The distance between points C and the origin is 17 units.