Question

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'.

Answer 1

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`