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?
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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)
To determine the coordinates of the vertices of the triangle, you need to add the vector PA-P to point P. Similarly, you need to add the vector PB-P to point P.
To subtract vectors, you subtract each corresponding component individually. So, for example, to subtract vector A=(X2, Y2, Z2) from vector B=(X1, Y1, Z1), you would subtract X2 from X1, Y2 from Y1, and Z2 from Z1.
Let's calculate the coordinates of the vertices using the given vectors and point:
The first vertex can be obtained by adding the vector PA-P to point P:
P1 = P + (PA - P)
= (1, 3, 2) + (-1, -4, -1)
= (1, 3, 2) + (-1, -4, -1)
= (0, -1, 1)
The second vertex can be obtained by adding the vector PB-P to point P:
P2 = P + (PB - P)
= (1, 3, 2) + (-5, 1, 0)
= (1, 3, 2) + (-5, 1, 0)
= (-4, 4, 2)
So, the coordinates of the vertices of the triangle are:
P1 = (0, -1, 1)
P2 = (-4, 4, 2)