Question 124
Let $ABCD A_{1} B_{1} C_{1} D_{1}$ be a cube. The point $K$ is an interior point of the edge $B B_{1}$ such that $BK / K B_{1} = m$. Through the points $K$ and $C_{1}$ a plane $\alpha$ is drawn, parallel to the line $B D_{1}$.
a. Let $P$ be the intersection point of the plane $\alpha$ with the line $A_{1} B_{1}$. Find the value of the ratio $A_{1} P / P B_{1}$.
b. The plane $\alpha$ divides the cube into 2 parts. Find the ratio of the volumes of these parts.
a. Let $P$ be the intersection point of the plane $\alpha$ with the line $A_{1} B_{1}$. Find the value of the ratio $A_{1} P / P B_{1}$.
b. The plane $\alpha$ divides the cube into 2 parts. Find the ratio of the volumes of these parts.