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

*(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

*(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).)*

You can earn partial credit on this problem.