Consider the vectors a = 5 I + j - j b = -I -5 j + k c = I -5j d = 5i - j + k g
ID: 2855607 • Letter: C
Question
Consider the vectors a = 5 I + j - j b = -I -5 j + k c = I -5j d = 5i - j + k g = I + 5j -k. Which pairs (if any) of these vectors are Are perpendicular? (Enter none or a pair or list of pairs e. g, if a is perpendicular to b and c enter (a, b) (a,c)) Are parallel? (Enter none or a pair or list of pairs e. g if a is parallel to b and c enter (a, b) (a, c)) Have an angles less than pi/2 between them? (Enter none or a pair or list of pairs e. g if a is at an angle less than pi/s from b and 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, e. g if a is at an angle greater than pi/2 from b and c enter (a, b) (a, c))Explanation / Answer
Solution:
a = 5i + j - k, b = -i - 5j + k, c = i - 5j
d = 5i - j + k, g = i + 5j - k
a). Which pairs are perpendicular?
The ones whose dot products are zeros:
(a,c)
b).Which pairs are parallel?
(Note that this will include "anti-parallel" pairs.)
The ones that are linear multiples of each other:
(b,g)
c).Which pairs have an angle less than pi/2 between them?
The ones with positive dot-products:
(a,d), (a,g), (b,c), (b,d), (c,d)
d).Which pairs have an angle greater than pi/2 between them?
The ones with negative dot-products:
(a,b),(b,g),(c,g), (d,g)