which are skew lines?
a and b
a and d
b and d

Question

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "direct_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Skew Lines" ], "new_concepts": [], "current_concepts": [ "Skew Lines", "Coplanar Lines", "3D Geometry" ] } ## Identify the geometric relationships of the lines $$ \begin{aligned} &\text{Line } a \text{ lies entirely in plane } N.\ &\text{Line } b \text{ lies entirely in plane } N \text{ and intersects line } a.\ &\text{Line } c \text{ lies in a vertical plane intersecting plane } N.\ &\text{Line } d \text{ is the line of intersection of the two planes, intersecting line } c. \end{aligned} $$ ## Evaluate the options for skew lines $$ \begin{aligned} &\text{Lines } a \text{ and } b \text{ are coplanar (both in plane } N\text{) and intersect } \implies \text{not skew.}\ &\text{Lines } b \text{ and } d \text{ are coplanar (both in plane } N\text{) and parallel } \implies \text{not skew.}\ &\text{Lines } a \text{ and } d \text{ lie in different planes, are not parallel, and do not intersect } \implies \text{skew.} \end{aligned} $$

a and b

a and d

b and d

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Skew Lines" ] }

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Question

Explanation:

Identify the geometric relationships of the lines

Evaluate the options for skew lines

Answer: