A Geometric Implication

Geometry Level 5

Let $P_{1}$ be a plane determined by the vectors $A$ and $B$ . Plane $P_{2}$ be determined by vectors $C$ and $D$ . Plane $P_{3}$ be determined by vectors $A$ and $C$ . Plane $P_{4}$ be determined by vectors $B$ and $D$ . If $L_{1}$ represents the line of intersection (direction) of planes $P_{1}$ and $P_{2}$ , and $L_{2}$ represents the line of intersection(direction) of $P_{3}$ and $P_{4}$ . The vector along the direction of $L_{1} \times L_{2}$ is given by,

((A \times B)\times(C \times D))\times((A\times C)\times(B\times D))

((A \times B)\times(C \times D))

((B \times D)\times(C \times D))\times((A\times C)\times(B\times D))

((B \times C)\times(C \times D))\times((A\times D)\times(B\times C))

((B \times D)\times(C \times D))\times((A\times C)\times(B\times C))

1 solution

Suhas Sheikh
Jun 9, 2018

Choose a few unit trial vectors And bash the options out It isn't elegant but it works :P

A Geometric Implication

1 solution

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