If "u = (2,2,-1)", "v = (3,-1,0)" and "w = (1,7,8)", verify that "u (dot) (v + w) = u (dot) v + u (dot) w".

My work:

LHS:
u (dot) (v + w)
= (2,2,-1) (dot) (4,6,8)
= [(2,2,-1) (dot) (3,-1,0)] + [(2,2,-1) (dot) (1,7,8)]
= [u (dot) v] + [u (dot) w]
Therefore, LHS = RHS

Did I prove this question correctly?

You should calculate the numerical values for each side and show that thay are the same.

12 (left side)= 4 + 8 (right side)

Although the give you specific numerical values for u, v and w, the relationship is true in general.

Yes, you have correctly proven the statement "u (dot) (v + w) = u (dot) v + u (dot) w".

You started by finding the dot product of the vector u with the vector (v + w).
Then, you expanded this dot product by using the distributive property of the dot product over vector addition.
Finally, you used the dot product of u with v and u with w separately to complete the equation. By showing that the left-hand side (LHS) equals the right-hand side (RHS), you have successfully proven the given statement. Well done!