Find Parametric Equations for the Line Through the Point $( 5,6,3 )$

question 112

Multiple Choice

Find parametric equations for the line through the point $( 5,6,3 )$ that is parallel to the plane $x + y + z = - 15$ and perpendicular to the line $x = 15 + t , y = 12 - t , z = 3 t$ .
Select the correct answer.

• A) \(\quad x = 4 t + 5 , y = - 2 t + 6 , z = - 2 t + 3\)
• B) \(x = 4 t , y = - 2 t + 6 , z = - 2 t\)
• C) \(x = 4 t + 2 , y = - 2 t + 6 , z = - 2 t + 3\)
• D) \(x = 4 t + 2 , y = - 2 t + 6 , z = 0\)
• E) \(x = 4 t , y = - 2 t , z = - 2 t + 3\)

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