Problem $1$: Consider the plane defined by the equation $\backslash (2$ x$-5$ y$+10$ z$+60=0\backslash ).$

a$)$ Use MATLAB and the surf$()$ function to plot the plane over the interval $\backslash ($ x $\backslash$in$[-2,2]\backslash ),\backslash ($ y $\backslash$in$[-2,2]\backslash ).$ Choose an appropriate view to best visualize the plane and label axes appropriately.

Solution:

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b$)$ Where does the plane intersect the x $-$axis, y $-$axis, and z $-$axis? Provide a coordinate $(\backslash ($ x$,$ y$,$ z $\backslash ))$ for each intersection.

Solution:

Put your math$/$explanation here...

c$)$ Compute the normal vectorn to the plane. Express $\backslash ($ n $\backslash )$ in terms of the standard unit vectors $\backslash (\backslash$mathbf$\{$i$\},\backslash$mathbf$\{$j$\}\backslash ),$ and $\backslash (\backslash$mathbf$\{$k$\}\backslash ).$

Solution:

Put your math$/$explanation here...

d$)$ Use MATLAB to plot the plane $($as in part $($a$))$ and a normal vector to the plane using the surfnorm $0$ function at the point $\backslash ((0,0,-6)\backslash ).$ Normalize and scale the surfnorm$()$computed vector to show it equals the value found in part $($c$).$ Make sure to use the axis equal command so the plane and vector look orthogonal as desired.

Solution:

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