Question $12$: $4$ Marks

$(12\mathrm{.}1)$ Let $U$ and $Vbe$ the planes defined $by$ the equations:

$U$:$x+5y-2z-3=0$

$V$:$-x+y+2z+1=0$

where $inRis$ a parameter.

$(a)$ Determine all values $offor$ which the planes $U$ and $V$ are orthogonal.

$(b)$ Determine all values $offor$ which the planes $U$ and $V$ are parallel.

$(c)$ For $=2,$ find the parametric equations $of$ the line $of$ intersection between the two

planes.

$(d)$ For $=1,$ find the angle between the two planes.