Question

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

Answer 1

Are you sure your points are correct?

None of the line segments form parallel lines, (slopes are not equal)

Answer 2

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]

Answer 3

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.