Which of the following statements are true? I. The shortest distance between two skew lines is along the line perpendicular to both. II. If ( a₂ - a₁) · ( b₁ × b₂) = 0 for non-parallel lines, the lines intersect. III. Two parallel lines are skew. IV. Two skew lines always lie in one plane.

Question 91

MediumOriginal question

Which of the following statements are true?
I. The shortest distance between two skew lines is along the line perpendicular to both.
II. If $(\vec{a}_2 - \vec{a}_1) \cdot (\vec{b}_1 \times \vec{b}_2) = 0$ for non-parallel lines, the lines intersect.
III. Two parallel lines are skew.
IV. Two skew lines always lie in one plane.

I and II onlyCorrect answerYour answerI, II and III onlyCorrect answerYour answerII and IV onlyCorrect answerYour answerI, II and IV onlyCorrect answerYour answer

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CorrectNot quiteAnswer A

Correct answer: A

I and II are true: the formula measures along $\vec{b}_1 \times \vec{b}_2$ , and a zero numerator means distance 0.
III and IV are false: parallel lines lie in a plane, and skew lines never do.

Concept: Facts about skew lines
Typical timeTypical: 120 s
Your timeYours: —

The rule this testsSkew lines and the shortest distance

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