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 1

Multiple Choice

Find the parametric equation of the plane through the point (-4, 2, 4) 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) \(x = - 4 - 2 u - 4 v , y = 2 + 2 u + 4 v , z = 4 - 4 u - 2 v\)
• B) \(x = - 4 - 2 u - 4 v , y = 2 + 2 u + 4 v , z = 4 + 4 u - 2 v\).
• C) \(x = - 4 - 2 u + 4 v , y = 2 + 2 u - 4 v , z = 4 - 4 u + 2 v\)
• D) \(x = - 2 u - 4 v , y = 2 u + 4 v , z = - 4 u - 2 v\)
• E) \(x = - 4 - 2 u - 4 v , y = 2 + 2 u + 4 v , z = 4 - 4 u - 2 v\)..

---

Definitions:

Setup Cost

The initial expense required to create a new product or establish a new process, including costs for equipment, facilities, and labor.

Multiply

The mathematical operation of increasing a number by another specified number of times, essentially repeated addition.

Multiply

To perform a mathematical operation where a number is added to itself a certain number of times, represented by the symbol \(*\).

Simplify

The process of altering an expression to make it easier to read or work with, typically by combining like terms and using algebraic properties.