Answer:
The angle between vector and is approximately radians, which is equivalent to approximately .
Explanation:
The angle between two vectors can be found from the ratio between:
To be precise, if denotes the angle between and (assume that or equivalently ,) then:
.
The first component of is and the first component of is also
The second component of is while the second component of is . The product of these two second components is .
The dot product of and will thus be:
Apply the Pythagorean Theorem to both and :
Let represent the angle between and . Apply the formula to find the cosine of this angle:
Since is the angle between two vectors, its value should be between and ( and .) That is: and . Apply the arccosine function (the inverse of the cosine function) to find the value of :
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