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If A=(-1,1), B=(5,-2), C=(2,3), D=(a,5) and vector AB is parallel to vector DC, find the value of 'a'.
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If A=(-1,1), B=(5,-2), C=(2,3), D=(a,5) and vector AB is parallel to vector DC, find the value of 'a'.

User Apostolov
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1 Answer

5 votes

Answer:

a = 3

Explanation:


\vec{AB} = <6; -3>\\\vec{DC} = <2-a, 3 - 5> = <2-a, -2>\\\vec{AB} \perp \vec{DC} => \vec{AB} \cdot \vec{DC} = 0 = 6(2-a) + (-3)(-2) = 0\\12 - 6a + 6 = 0\\6a = 18\\a = 3

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