The planes ${{\mathrm{p}}_{1}}$ and ${{\mathrm{p}}_{2}}$ have equations \(\mathbf{r}\cdot \left(

Question

The planes ${{\mathrm{p}}_{1}}$ and ${{\mathrm{p}}_{2}}$ have equations $\mathbf{r}\cdot \left( \begin{matrix}3 \ -2 \-3 \\end{matrix} \right)=4$ and $\mathbf{r}\cdot \left( \begin{matrix} 4 \ 5 \-4 \\end{matrix} \right)=2$ respectively, and meet in the line ${{l}_{4}}$. Find the vector equation for ${{l}_{4}}$, Find the acute angle between ${{\mathrm{p}}_{1}}$ and ${{\mathrm{p}}_{2}}$.

Accepted Answer

(i) $\mathbf{r}=\frac{1}{23}\left( \begin{matrix} 24 \ -10 \ 0 \ \end{matrix} ight)+\gamma \left( \begin{matrix} 1 \ 0 \ 1 \ \end{matrix} ight);\gamma \in \mathbb{R}$ (ii) $66.7{}^\circ $

Vectors - Angle Between Two Planes

Vectors - Angle Between Two Planes

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