Determine for each of the following pairs of line and plane, whether the line $l$ intersects the pla

Question

Determine for each of the following pairs of line and plane, whether the line $l$ intersects the plane $\prod $ at a unique point, lies on the plane or do not intersect the plane. If the line intersects the plane at a unique point, find the point of intersection and the acute angle between the $l$ and $\prod $. $\prod :\mathbf{r}\cdot \left( \begin{matrix} 2 \ 1 \ -3 \ \end{matrix} ight)=5$ and $l:\mathbf{r}=\left( \begin{matrix} 3 \ -1 \ 1 \ \end{matrix} ight)+\lambda \left( \begin{matrix} -2 \ 1 \ -3 \ \end{matrix} ight)$, $\lambda \in \mathbb{R}$. $\prod :\mathbf{r}\cdot \left( \begin{matrix} 2 \ 1 \ -3 \ \end{matrix} ight)=5$ and $l:\mathbf{r}=\left( \begin{matrix} 2 \ 1 \ 0 \ \end{matrix} ight)+\lambda \left( \begin{matrix} 1 \ 1 \ 1 \ \end{matrix} ight)$, $\lambda \in \mathbb{R}$.

Accepted Answer

(i) Point: (-2/3, -1/3, 5/3), Angle: 54.7°; (ii) Line lies on plane, Angle: 0°

CJC Vectors Tutorial Q2

CJC Vectors Tutorial Q2

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