$\tiny{s4.854.13.5.47}$

$\textsf{a. Find symmeteric equations for the line of intersection of planes}\\$

$\textsf{b. Find the angle between the planes}\\$

\begin{align}\displaystyle

j+y-z&=2 \\

3x-4y+5z &=6

\end{align}

\begin{align}\displaystyle

n_1&=\langle 1,1,-1\rangle\\

n_2&=\langle 3,-4,+5\rangle

\end{align}

\begin{align}

\displaystyle

\frac{n_1\cdot n_2}{|n_1||n_2|}

&=\frac{3(1)+(-4)(1)+5(-1)}{\sqrt{3}\sqrt{50}}\\

&=\frac{\sqrt{6}}{5}\\

\cos^{-1}\left({\frac{\sqrt{6}}{5}}\right)

&=119^o \textit{or} \, 61^o

\end{align}

\begin{align}

\begin{bmatrix}

i & j & k\\

1 &1 &-1\\

3 &-4 &5

\end{bmatrix} &=\textbf{i-8j-7k}

\end{align}

$\textsf{the symmetric equations are:}$

\begin{align}

x-2&=\frac{y}{(-8)}=\frac{z}{(-7)}

\end{align}

suggestions?