Consider the vectors $$\vec a = 2\,\mathit{\vec i}+\,\mathit{\vec j}-\,\mathit{\vec k}, \qquad \vec b = \vec{i} +2 \vec{j} + \vec{k}, \qquad \vec c = \,\mathit{\vec i}-2\,\mathit{\vec j}$$ $$\vec d = -\,\mathit{\vec i}-2\,\mathit{\vec j}+\,\mathit{\vec k},\qquad \vec g = 2\,\mathit{\vec i}-\,\mathit{\vec j}+\,\mathit{\vec k}.$$ Which pairs (if any) of these vectors are

(a) Are perpendicular?

(Enter none or a pair or list of pairs, e.g., if $\vec a$ is perpendicular to $\vec b$ and $\vec c$, enter (a,b),(a,c).)

(b) Are parallel?

(Enter none or a pair or list of pairs, e.g., if $\vec a$ is parallel to $\vec b$ and $\vec c$, enter (a,b),(a,c).)

(c) Have an angles less than $\pi/2$ between them?

(Enter none or a pair or list of pairs, e.g., if $\vec a$ is at an angle less than pi/2 from $\vec b$ and $\vec c$, enter (a,b),(a,c).)

(d) Have an angle of more than $\pi/2$ between them?

(Enter none or a pair or list of pairs, e.g., if $\vec a$ is at an angle greater than pi/2 from $\vec b$ and $\vec c$, enter (a,b),(a,c).)