Finding the smallest angle between Vectors

AI Thread Summary
To find the smallest angle between vectors A (2i + j + 3k) and B (-2j + 2k), the dot product can be used, treating B as (0i - 2j + 2k). The cosine of the angle is derived from the dot product formula, which remains valid regardless of the vectors' dimensionality. The term "smallest angle" is misleading, as there is only one angle between two vectors, determined through the dot product. Therefore, the focus should be on calculating the angle using the correct method rather than the terminology.
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Vectors Angles

How do you find the smallest angle between vectors? This one is tricky because 1 vector and 3 values and the other has 2.

A (2i+j+3k) and B (-2j+2k)

Thanks,

Pamela
 
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It doesn't matter, the dot product is still the same. think of the 2nd vector as (0i-2j+2k) and compute the cosine between the vectors.
 
In addition, there is no smallest angle between two vectors ; there can be only one angle (given through the dot product).
"Smallest angle" is a poor term since it almost implies that there exist other angles.
 
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