Consider the vectors u=−2i+5j+8k\mathbf{u} = -2\mathbf{i} + 5\mathbf{j} + 8\mathbf{k}u=−2i+5j+8k and v=xi+yj+zk\mathbf{v} = x\mathbf{i} + y\mathbf{j} + z\mathbf{k}v=xi+yj+zk.
Given that the sum of vectors u\mathbf{u}u and v\mathbf{v}v is −7i−j+3k-7\mathbf{i} - \mathbf{j} + 3\mathbf{k}−7i−j+3k, determine the values of xxx, yyy, and zzz.
