How components of v and w add to zero

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Every combination of v = (1,-2,1) and w = (0,1 ,-1) has components that add to? Find c and d so that cv+ dw = (3,3,-6). Why is (3,3,6) impossible? (Source: Gilbert Strang Introduction to Linear Algebra).

In the solution manual, it is given: The components of every cv + dw add to zero because the components of v and of w add to zero. c = 3 and d = 9 give (3, 3,−6). There is no solution to cv+dw = (3, 3, 6) because 3 + 3 + 6 is not zero.

So it is given the components of v and of w add to zero.

I find v + w = (1,-1,0). So not sure how v + w = 0 in this context.

https://math.stackexchange.com/questions/4354014/how-components-of-v-and-of-w-add-to-zero

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