Determine Whether the Lines Given Below Intersect, And, If So

question 51

Multiple Choice

Determine whether the lines given below intersect, and, if so, find the point of intersection. $$\begin{array} { l } \frac { x - 1 } { 5 } = \frac { y - 2 } { 7 } = \frac { z + 8 } { 5 } \\\frac { x - 3 } { 1 } = \frac { x - 15 } { - 2 } = \frac { z - 5 } { - 2 }\end{array}$$

• A) The lines are parallel.
• B) The lines intersect at \(( 2,6 , - 33 )\).
• C) The lines intersect at \(( 7,11 , - 3 )\).
• D) The lines intersect at \(( 6,9 , - 1 )\).
• E) The lines are not parallel but do not intersect.

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Definitions:

Anticline

A type of fold that is arched upward and has its oldest beds at its core, often associated with oil and gas reservoirs.

Syncline

A fold in rock layers that dips downwards, where the youngest layers are at the core of the fold.

Monocline

A type of geological fold in which all layers are inclined in the same direction; it is an example of a simple bend in rock layers.

Lineation

A linear structure in a metamorphic rock.