Find Parametric Equations for the Line Through the Point $( 3,4,5 )$

question 46

Short Answer

Find parametric equations for the line through the point $( 3,4,5 )$ that is parallel to the plane $x + y + z = - 15$ and perpendicular to the line $x = 15 + t , y = 12 - t , z = 3 t$ .

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Definitions:

Functional Redundancy

The phenomenon where multiple species or genes perform similar functions within an ecosystem or biological system, providing resilience against environmental changes or perturbations.

Engrailed Gene

A gene that plays a crucial role in defining the segments and patterning of the body parts in many organisms, including their limb development.

Paralog

A paralog is a homologous gene that arises by gene duplication. Paralogs together form a gene family.

Ortholog

An ortholog is one of two or more homologous genes separated by a speciation event (as opposed to paralogs — homologous genes, produced by gene duplication, that are both possessed by the same species).