Math  vector equation of a parallelogram
posted by Shaila .
The vertices of a parallelogram are the origin and the points A(1,4), B(3,6), and C(7,2). Write the vector equations of the lines that make up the sides of the parallelogram

Are you sure your points are correct?
None of the line segments form parallel lines, (slopes are not equal) 
Isn't there another way to find the vector equation because they are the correct coordinates sample answers are:
[x,y]=[1,4]+t[1,1]
[x,y]=[1,4]+t[2,1] 
Sure, we can find the vector equations of those lines, but I hesitated since you called it a parallelogram, which it isn't.
let's find vector equation for line BC
direction vector of BC is [4,4] or simplified to [1,1)
a point on there is {3,6)
equation for BC:
[x,y] = (3,6) + t(1,1)
I still think there is something wrong with your question.