The position vector of $C$ is $-3\vec i - 2\vec j + p\vec k$.
Show that, if $p$ is a variable, then the locus of $C$ is a straight line and find the two unit direction vectors along this line.
Intuitively I think that the locus will be along the unit k vector. But I am not able to figure out how to go about proving this.
Can you guys point me in the right direction? Thanks for your help.