The trajectory of a weather balloon, lAl_AlA, and a monitoring drone, lBl_BlB, are modeled as lines in 3D space relative to a fixed ground station at the origin OOO. The equations of the paths are given by:
lA:r=(1−12)+λ(213) l_A : \mathbf{r} = \begin{pmatrix} 1 \\ -1 \\ 2 \end{pmatrix} + \lambda \begin{pmatrix} 2 \\ 1 \\ 3 \end{pmatrix} lA:r=1−12+λ213 lB:r=(50−3)+μ(1−2k) l_B : \mathbf{r} = \begin{pmatrix} 5 \\ 0 \\ -3 \end{pmatrix} + \mu \begin{pmatrix} 1 \\ -2 \\ k \end{pmatrix} lB:r=50−3+μ1−2kwhere λ\lambdaλ and μ\muμ are scalar parameters and kkk is a constant.
Show that for all values of k≠−26k \neq -26k=−26, the paths lAl_AlA and lBl_BlB are skew.
