Given The points $A,B,C,D$ which forms a parallelogram with adjacent sides $AB, AC$ and vertices, Find the coordinates of $D$, given those of $A,B,C$

Question

I am new to this, how do i use vectors to find the points of the last vertex?

Given the points: $A,B,C$ and $D$ forms a parallelogram with adjacent sides $AB$ and $AC$ and vertices $A = (5,0,0) ,B = (0,1,0), C = (0,0,4)$.

Find the coordinates of $D$

Appreciate the assistance.

Answer 1

Hint:

A parallelogram has two pairs of parallel sides equal, so either $A - B$ = $C - D$, or $A - C = B - D$.

Answer 2

Hint: It must be $$\vec{AB}=\vec{DC}$$ so you will get $$[-5;1;0]=[0-x_D;0-y_D;4-z_D]$$ Can you finish?

Answer 3

Or, as you may know from physics: $$\vec{AB}+\vec{AC}=\vec{AD}$$