The trajectory of a weather balloon, $l_A$ , and a monitoring drone, $l_B$ , are modeled as lines in 3D space relative to a fixed ground station at the origin $O$ . The equations of the paths are given by:

l_A : \mathbf{r} = \begin{pmatrix} 1 \\ -1 \\ 2 \end{pmatrix} + \lambda \begin{pmatrix} 2 \\ 1 \\ 3 \end{pmatrix}

l_B : \mathbf{r} = \begin{pmatrix} 5 \\ 0 \\ -3 \end{pmatrix} + \mu \begin{pmatrix} 1 \\ -2 \\ k \end{pmatrix}

where $λ\lambda$ and $μ\mu$ are scalar parameters and $k$ is a constant.

Show that for all values of $\neq -26$ , the paths $l_A$ and $l_B$ are skew.

l_A : \mathbf{r} = \begin{pmatrix} 1 \\ -1 \\ 2 \end{pmatrix} + \lambda \begin{pmatrix} 2 \\ 1 \\ 3 \end{pmatrix}

l_B : \mathbf{r} = \begin{pmatrix} 5 \\ 0 \\ -3 \end{pmatrix} + \mu \begin{pmatrix} 1 \\ -2 \\ k \end{pmatrix}

where $λ\lambda$ and $μ\mu$ are scalar parameters and $k$ is a constant.

Show that for all values of $\neq -26$ , the paths $l_A$ and $l_B$ are skew.

1.10 Vectors

Question 42

Markscheme

1.10 Vectors

Question 42

Markscheme

1.10 Vectors

Question 42

1.10 Vectors Questions

1.10 Vectors

Question 42

1.10 Vectors Questions