Do the Two Lines $\mathrm { x } _ { 1 } ( t ) = \langle 1,1,3 \} + t ( - 1,0,2 \}$

question 191

Essay

Do the two lines $\mathrm { x } _ { 1 } ( t ) = \langle 1,1,3 \} + t ( - 1,0,2 \}$ and $\mathrm { x } _ { 2 } = \langle - 1,1,4 \rangle + s \langle 2,0,1 \}$ intersect? If so, find the point of intersection.

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Definitions:

Diaphysis

The shaft or central part of a long bone.

Epiphyseal Lines

The remnants of the epiphyseal plate (growth plate) in long bones, indicating where bone growth occurred.

Articular Cartilage

A creamy, white covering on the ends of bones at junctions, designed to lower friction and absorb impact.

Epiphysis

The end part of a long bone, which is initially growing separately from the shaft.