高考数学：空间向量与立体几何
A high-school mathematics practice set on spatial vectors and solid geometry: vector coordinates, dot and cross products, distance from a point to a plane, plane equations from a normal vector, and line-plane angle relationships.
- Compute the distance from a point to a plane using a normal vector
- Determine whether two non-zero vectors are perpendicular or collinear
- Derive a plane's equation from a point and its normal vector
- Calculate the sine of the angle between a line and a plane
高考数学：空间向量与立体几何 — 空间向量坐标、数量积、夹角、法向量与空间距离。
示例问题
在空间中，点 $P(1, 2, 3)$ 到平面 $x+y+z-6=0$ 的距离是多少？
- $0$
- $1$
- $\sqrt{3}$
- $2$
查看答案
$0$
点到平面的距离公式为 $d = \frac{|Ax_0+By_0+Cz_0+D|}{\sqrt{A^2+B^2+C^2}}$。代入得 $d = \frac{|1+2+3-6|}{\sqrt{1^2+1^2+1^2}} = 0$。