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

Question

The planes ${{\mathrm{p}}_{1}}$ and ${{\mathrm{p}}_{2}}$ have equations $\mathbf{r}\cdot \left( \begin{matrix}1 \ -3 \ 2 \\end{matrix} ight)=-5$ and $\mathbf{r}\cdot \left( \begin{matrix} 2 \-1 \ 3 \\end{matrix} ight)=1$ 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) $\mathbf{r} = \begin{pmatrix} 8/5 \\ 11/5 \\ 0 \end{pmatrix} + \lambda \begin{pmatrix} -7/5 \\ 1/5 \\ 1 \end{pmatrix}$; (ii) $38.2^\circ$

Unit 13.2 Worked Example 5

Unit 13.2 Worked Example 5

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