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How do you find the acute angle between two intersecting lines whos equations are given in vector form?

For this question we first need to understand which angle it is we're calculating. When two lines intersect two pairs of equal and opposite angles are formed (4 angles total). We are looking to find the small of these two angle values.
To do this, we use the rearranged dot product formula. Only the direction parts of the line equations are needed - this is the part next to the scalar multiplier. We find the dot product of these two direction vectors as well as their magnitudes and then substitute these into the formula. Then we can use the inverse cosine function to give us the angle we're looking for.