Q$-1($LO$1)$

$10$ a$)$ The points $P(0,2,4)$ and $Q(-3,1,5)$ are given in the cartesian coordinates. Write vector vec$(PQ).$

$15$ b$)$ A point $P(-3,4,2)$ is given in cartesian coordinates. Write point $P(,,z)$ and the position vector vec$(r{)}_P$ of the point $P(-3,4,2)$ in the cylindirical coordinates.

$($Information:

$x=cos()$;$,=\sqrt[\phantom{2}]{x^2+y^2}$;$,$

$y=sin()$;$,cos()=\frac{x}{}$;$,$hat$()=cos()hat()-sin()hat()$;

$z=z,sin()=\frac{y}{}$;$,$hat$()=sin()hat()+cos()hat()$

$,tan()=\frac{y}{x}$;$,$