&#92；[ &#92；sqrt{(-1/2)^2+(1/2)^2+(-1/2)^2+k^2}=1 &#92；]。化简得。&#92；[ &#92；sqrt{1/4+1/4+1/4+k^2}=1 &#92；]。进一步得到。&#92；[ 1/4+1/4+1/4+k^2=1 &#92；]。合并同类项。&#92；[ 3/4+k^2=1 &#92；]。移项并求解k。&#92；[ k^2=1-3/4 &#92；]。&#92；[ k^2=1/4 &#92；]。开平方。&#92；[ k=1/2 &#92；] 或 &#92；[ k=-1/2 &#92；]。综上所述，k的值可以是1/2或-1/2。