求使下列方程组有唯一解的 $k$ 值集合，并从几何角度解释这一情形：

Answer all questions. You should use a calculator where appropriate.

You must show all necessary working clearly; no marks will be given for unsupported answers from a calculator.

Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless a different level of accuracy is specified in the question.

请回答所有题目。适当时应使用计算器。必须清楚展示所有必要的计算过程；仅给出计算器答案而没有过程，不予评分。除非题目另有精度要求，非精确数值答案保留 3 位有效数字，以度为单位的角度保留 1 位小数。

求系数矩阵的行列式，并排除使它为零的参数。方程组的唯一解就是三个平面的唯一公共点。

The coefficient determinant is

There is a unique solution when $\boxed{k\in\mathbb R\setminus\{\frac78\}}$. Geometrically, the three planes meet at exactly one point.