Consider the following vectors. a = i? 3 j? k b = i + j + 2k c= -2i-j+k d = ? i
ID: 3139290 • Letter: C
Question
Consider the following vectors.a = i? 3 j? k
b = i + j + 2k
c= -2i-j+k
d = ? i ?j + k
Determine which pairs (if any) satisfy the given conditions. (Select all that apply.)
(a) Which pairs are perpendicular?
a and b
a and c
a and d
b and c
b and d
c and d
no pairs
(b) Which pairs are parallel?
a and b
a and c
a and d
b and c
b and d
c and d
no pairs
(c) Which pairs have an angle less than ?/2 between them?
a and b
a and c
a and d
b and c
b and d
c and d
no pairs
(d) Which pairs have an angle more than ?/2 between them?
a and b
a and c
a and d
b and c
b and d
c and d
no pairs
Explanation / Answer
1)for perpendicular : dot product =0 pair a and c pair b and d 2)for parallel, unit vector must be same no pairs 3)angle less than pi/2 : dot product positive a and d c and d 4)angle more than pi/2 :dot product negative: a and b b and c