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) \(x = 4 t + 3 , y = - 2 t + 4 , z = - 2 t + 5\)

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Definitions:

Puerto Rico

An island territory of the United States located in the Caribbean Sea, with a rich blend of cultural influences and its own distinct identity.

Commonwealth

A political community founded for the common good, often used to describe self-governing territories associated with a larger nation.

United States

A country located in North America, consisting of 50 states, and known for its significant cultural and political influence globally.

Assimilation Model

A theory or approach suggesting that cultural or ethnic minorities should be absorbed into the dominant society, losing their original identities.