I am bit of confused from this question. I have shown the work below and to subtract, am I supposed to be X2 - X1, Y2-Y1, Z2-Z1? or X1-X2, Y1-Y2, Z1-Z2?
------------------------------------
A triangle has sides formed by the vectors PA=(2,7,3) and PB=(6,2,2). The point P=(1,3,2). Determine the coordinates of the vertices.
Here is what I have done.
PA-P=(2,7,3)-(1,3,2)
=(-1,-4,-1)
PB-P=(6,2,2) - (1,3,2)
=(-5,1,0)
We used to write vectors with [ ] brackets to avoid confusion with points
let point A be (a,b,c), point P is (1,3,2)
then vector PA = [a-1 , b-3 , c-2) = [2 , 7 , 3]
a-1 = 2 ---> a = 3
b-3 = 7 ---> b = 10
c-2 = 3 ---> c = 5
check: for A(3,10,5) and P(1,3,2)
vector PA = [2,7,3]
do the other in the same way
Why add?
Where do you see me adding.
in
vector PA = [a-1 , b-3 , c-2} = [2 , 7 , 3]
I even showed my subtraction of the numbers very explicitly.
Furthermore in my check to prove my answer is correct, you can see that I subtracted the values to get the original vector [2,7,3]
Sorry for the confusion. May I ask why my answer does not work? :S its asking for the vertices, not equal to Point P.
To determine the coordinates of the vertices of the triangle, you need to add the vectors (PA - P) and (PB - P) to the point P.
To subtract vectors, you subtract the corresponding components of the vectors. So, to find (PA - P), you subtract the x-components, y-components, and z-components separately.
For (PA - P),
X2 - X1 = 2 - 1 = 1
Y2 - Y1 = 7 - 3 = 4
Z2 - Z1 = 3 - 2 = 1
Therefore, (PA - P) = (1, 4, 1)
For (PB - P),
X2 - X1 = 6 - 1 = 5
Y2 - Y1 = 2 - 3 = -1
Z2 - Z1 = 2 - 2 = 0
Therefore, (PB - P) = (5, -1, 0)
Now, to determine the coordinates of the vertices, you add (PA - P) and (PB - P) to the point P.
Vertex A = P + (PA - P) = (1, 3, 2) + (1, 4, 1) = (2, 7, 3)
Vertex B = P + (PB - P) = (1, 3, 2) + (5, -1, 0) = (6, 2, 2)
So, the coordinates of the vertices of the triangle are:
Vertex A = (2, 7, 3)
Vertex B = (6, 2, 2)