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Solution

Vector $\vec v = x(\mathbf{i}+\mathbf{j}+\mathbf{k})$ Magnitude of unit vector $|\vec v|=1$ $|x(\mathbf{i}+\mathbf{j}+\mathbf{k})| =|x|\sqrt{1^2+1^2+1^2}$ $=|x|\sqrt{3}$ Since magnitude is 1 $|x|\sqrt{3}=1$ $|x|=\frac{1}{\sqrt{3}}$ Therefore $x=\pm\frac{1}{\sqrt{3}}$