We can write the lines general direction by vector notation as:
L1 = a1i + b1j and L2 = a2i + b2j
The dot product of these two vectors is related to the angle by the formula: L1 · L2 = |L1||L2|cos θ
Where:
L1 · L2 = a1a2 + b1b2 |
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Then the two possible angles are:
To find the angle bisector line equation, we use the distance equations:
And the two angle bisector lines equation are:
13(3x − 4y +2) = 5(5x + 12y + 1)
14x − 112y + 21 = 0
And the second line:
− 13(3x − 4y + 2) = 5(5x + 12y + 1)
64x + 8y + 31 = 0
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