Finding the acute angle between two lines (or between two vectors)

If we want to find the acute angle between two lines, we can convert the lines to standard vector form and then use the formula cos(theta)=(a•b)/(|a||b|), where a and b are the given vectors, a•b is the dot product of the vectors, |a| is the magnitude of the vector a (its length) and |b| is the magnitude of the vector b (its length).

Angle between two vectors

To find the angle between two vectors, we use a formula for cosine of the angle in terms of the dot product of the vectors and the magnitude of both vectors. The magnitude of each vector is given by the formula for the distance between points.

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