Find the Parametric Equation of the Plane Through the Point $\vec { r } ( t ) = ( 1 - 2 t ) \vec { i } + ( 5 + 2 t ) \vec { j } + ( 3 - 4 t ) \vec { k }$

question 17

Multiple Choice

Find the parametric equation of the plane through the point (5, 2, 2) and parallel to the lines $\vec { r } ( t ) = ( 1 - 2 t ) \vec { i } + ( 5 + 2 t ) \vec { j } + ( 3 - 4 t ) \vec { k }$ and $\vec { s } ( t ) = ( 3 - 4 t ) \vec { i } + 4 t \vec { j } + ( 4 - 2 t ) \vec { k }$
Select all that apply.

• A) \(x = 5 - 2 u - 4 v , y = 2 + 2 u + 4 v , z = 2 - 4 u - 2 v\)
• B) \(x = 5 - 2 u - 4 v , y = 2 + 2 u + 4 v , z = 2 + 4 u - 2 v\)
• C) \(x = 5 - 2 u + 4 v , y = 2 + 2 u - 4 v , z = 2 - 4 u + 2 v\)
• D) \(x = - 2 u - 4 v , y = 2 u + 4 v , z = - 4 u - 2 v\)
• E) \(x = 5 - 2 u - 4 v , y = 2 + 2 u + 4 v , z = 2 - 4 u - 2 v\).

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