Consider the cube ABCDEFGH represented below. We define the points I and J respectively by $\overrightarrow { \mathrm { HI } } = \frac { 3 } { 4 } \overrightarrow { \mathrm { HG } }$ and $\overrightarrow { \mathrm { JG } } = \frac { 1 } { 4 } \overrightarrow { \mathrm { CG } }$.
On the answer sheet provided in the appendix, to be returned with your work, draw, without justification, the cross-section of the cube by the plane (IJK) where K is a point of the segment [BF].
On the answer sheet provided in the appendix, to be returned with your work, draw, without justification, the cross-section of the cube by the plane (IJL) where L is a point of the line (BF).
Does there exist a point P on the line (BF) such that the cross-section of the cube by the plane (IJP) is an equilateral triangle? Justify your answer.
Consider the cube ABCDEFGH represented below.\\
We define the points I and J respectively by $\overrightarrow { \mathrm { HI } } = \frac { 3 } { 4 } \overrightarrow { \mathrm { HG } }$ and $\overrightarrow { \mathrm { JG } } = \frac { 1 } { 4 } \overrightarrow { \mathrm { CG } }$.
\begin{enumerate}
\item On the answer sheet provided in the appendix, to be returned with your work, draw, without justification, the cross-section of the cube by the plane (IJK) where K is a point of the segment [BF].
\item On the answer sheet provided in the appendix, to be returned with your work, draw, without justification, the cross-section of the cube by the plane (IJL) where L is a point of the line (BF).
\item Does there exist a point P on the line (BF) such that the cross-section of the cube by the plane (IJP) is an equilateral triangle? Justify your answer.
\end{enumerate}