**8/19/2014
**Given
vectors **a
= **2**i
–**
1**j**,
and **b
= **-½**i
**
+ ¼**j,
**find
the angle between them.

**Scroll
down for the solution.**

**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|
= ****√****2**^{2}**
****+
****1**^{2}**
= ****√****5
****and
****|b|
= ****√(****-½)**^{2}**
+ (¼)**^{2}**
= ****√****5/4.**