From here, students are typically told to just believe that the resulting vector has the following geometric properties.

从这里开始 学生们通常被告知只要相信得到的向量具有以下几何性质。

All that really matters here is that you'll end up with three different numbers that are interpreted as the coordinates of some resulting vector.

这里真正重要的是 你最终会得到三个不同的数 它们被解释为某个结果向量的坐标。

You can kind of imagine turning two different knobs to change the two scalers, defining the linear combination, adding the scaled vectors, and following the tip of the resulting vector.

你可以想象一下 转动两个不同的旋钮来改变两个标量 定义线性组合 将缩放的向量相加 然后沿着得到的向量的尖端移动。

However, in the unlucky case, where your two original vectors happen to line up, the tip of the resulting vector is limited to just this single line passing through the origin.

然而 在不幸的情况下 当你的两个原始向量恰好对齐时 结果向量的尖端仅限于这条穿过原点的直线。