Question

Write XY as the sum of unit vectors for X(8,2,-9)and Y(-12,-1,10).

First, express XY as an ordered triple. Then write the sum of the unit vectors i,j,and k.

XY = (-12,-1,10) - (8,2,-9)
= (-12-8,2-1,10-(-9)
= (-20,-3,19k)
= -20i+j+19k

Answer 1

I do not understand what you have done here at all.
XY does not mean much to me.
There are two kinds of products of vectors, cross product and dot product, X x Y and X dot Y.
There is also the sum of the vectors X + Y
It looks like you might mean the sum here, in which case you add the x, y and z components separately:
x component = 8 - 12 = -4
y component = 2 - 1 = 1
z component = -9 + 10 = 1
then answer = -4i + j + k