Question $3(20$ Marks$)$

$($a$)$ Calculate the angles that vector $H=3a_x+5a_y-8a_z$ makes $(6$ marks$)$

with the $x-,y-,$ and $z-$axes.

$($b$)$ Find the triple scalar product of $P,Q$ and $R,$ given that

$P=2a_x-a_y+a_z$

$Q=a_x+a_y+a_z$

$R=2a_x+3a_z$

$($c$)$ Simplify the following expression.

i$.A(AB).$

$(4$ marks$)$

ii$.A[A(AB)].$

$(4$ marks$)$