bac-s-maths 2016 QI.4

bac-s-maths · France · centres-etrangers 1 marks Vectors: Lines & Planes True/False or Verify a Given Statement
In space referred to an orthonormal coordinate system, consider the line $\mathscr{D}_1$ with parametric representation: $$\left\{ \begin{array}{l} x = 1 + 2t \\ y = 2 - 3t \\ z = 4t \end{array} \right., t \in \mathbb{R}$$
Statement 4: The line $\mathscr{D}_1$ is parallel to the plane with equation $x + 2y + z - 3 = 0$.
Indicate whether this statement is true or false, justifying your answer.
In space referred to an orthonormal coordinate system, consider the line $\mathscr{D}_1$ with parametric representation:
$$\left\{ \begin{array}{l} x = 1 + 2t \\ y = 2 - 3t \\ z = 4t \end{array} \right., t \in \mathbb{R}$$

\textbf{Statement 4:} The line $\mathscr{D}_1$ is parallel to the plane with equation $x + 2y + z - 3 = 0$.

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