bac-s-maths 2016 QI.3

bac-s-maths · France · centres-etrangers 1 marks Vectors 3D & Lines MCQ: Relationship Between Two Lines
In space referred to an orthonormal coordinate system, consider the lines $\mathscr{D}_1$ and $\mathscr{D}_2$ which have the following parametric representations respectively: $$\left\{ \begin{array}{l} x = 1 + 2t \\ y = 2 - 3t \\ z = 4t \end{array} \right., t \in \mathbb{R} \quad \text{and} \quad \left\{ \begin{array}{l} x = -5t' + 3 \\ y = 2t' \\ z = t' + 4 \end{array} \right., t' \in \mathbb{R}$$
Statement 3: The lines $\mathscr{D}_1$ and $\mathscr{D}_2$ are secant.
Indicate whether this statement is true or false, justifying your answer.
In space referred to an orthonormal coordinate system, consider the lines $\mathscr{D}_1$ and $\mathscr{D}_2$ which have the following parametric representations respectively:
$$\left\{ \begin{array}{l} x = 1 + 2t \\ y = 2 - 3t \\ z = 4t \end{array} \right., t \in \mathbb{R} \quad \text{and} \quad \left\{ \begin{array}{l} x = -5t' + 3 \\ y = 2t' \\ z = t' + 4 \end{array} \right., t' \in \mathbb{R}$$

\textbf{Statement 3:} The lines $\mathscr{D}_1$ and $\mathscr{D}_2$ are secant.

Indicate whether this statement is true or false, justifying your answer.