8/19/2014 Given vectors a = 2i – 1j, and b = -½i + ¼j, find the angle between them.
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8/19/2014
Solution.
The
angle between 2 vectors is given by: cos θ
= a·b
/ |a||b| where
a·b
is
the dot product, 2·-½
+ -1·¼
= -5/4
whereas
|a||b| is
the magnitude of both vectors. Now, |a|
= √22
+
12
= √5
and
|b|
= √(-½)2
+ (¼)2
= √5/4.
Therefore,
|a||b|
= 5/4.
Substituting,
we get: cos θ
= (-5/4) / (5/4) = -1 so that θ
= 180° suggesting that both vectors are parallel and lie in
opposite directions.