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

question 116

Multiple Choice

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 $x = 15 + t , y = 12 - t , z = 3 t$ .

• A) \(x = 4 t + 2 , y = - 2 t + 4 , z = - 2 t + 5\)
• B) \(x = 4 t + 2 , y = - 2 t + 4 , z = 0\)
• C) \(x = 4 t , y = - 2 t , z = - 2 t + 5\)
• D) \(x = 4 t , y = - 2 t + 4 , z = - 2 t\)
• E) \(x = 4 t + 3 , y = - 2 t + 4 , z = - 2 t + 5\)

---

Definitions:

Federal Health Insurance

Government-provided health insurance schemes in countries, often covering a large part of the population or specific groups, such as seniors or low-income individuals.

Entitlement

A right to benefits specified especially by law or contract.

Unemployment Insurance

A government program that provides financial assistance to unemployed workers who meet certain eligibility requirements.

Policy Formulation

The process by which governments or organizations develop strategies and guidelines to address specific issues or achieve certain objectives.