Consider the vectors rightarrow a 4 rightarrow I rightarro

Consider the vectors rightarrow a = 4 rightarrow I + rightarrow j - rightarrow k, rightarrow b = - 4 rightarrow I - rightarrow j + rightarrow k, rightarrow c = 4 rightarrow I - rightarrow j + rightarrow k rightarrow d = rightarrow I + rightarrow j + 5 rightarrow k, rightarrow g = - rightarrow I - 4 rightarrow j + rightarrow k. Which pairs (if any ) of these vectors are Are perpendicular? (Enter none or a pair or list of pairs, e.g., if rightarrow a is perpendicular to rightarrow b and rightarrow c, enter (a, b), (a, c).) Are parallel? (Enter none or a pair or list of pairs, e.g., if rightarrow a is perpendicular to rightarrow b and rightarrow c, enter (a, b), (a, c). ) Have an angles less than pi/2 between them? (Enter none or a pair or list of pairs or a pair or list of pairs, e.g., if rightarrow a is perpendicular to rightarrow b and rightarrow c, enter (a, b), (a, c).) Have an angle of more than pi / 2 between them ? ( Enter none or a pair or list of pairs, i.g., if rightarrow a is perpendicular to rightarrow b and rightarrow c, enter (a, b), (a, c).)

Solution

Perpendicular a and d; b and d and d and g Parallel : a and b c ) a and c ; b and g ; c and d ; c and g d) a and g ; b and c ; b and g