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

question 9

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:

Income Elasticity

A measure of how the demand for a good or service changes in relation to a change in income.

Good

A tangible product that satisfies human wants or needs.

Service

An (intangible) act or use for which a consumer, firm, or government is willing to pay.

Cross Elasticity

A measure of how the quantity demanded of one good responds to a change in the price of another good, indicating the relationship between goods as substitutes or complements.