Read the two statements and choose the correct option. I. Two lines with direction cosines l₁, m₁, n₁ and l₂, m₂, n₂ are perpendicular exactly when l₁l₂ + m₁m₂ + n₁n₂ = 0. II. The shortest distance between skew lines is | ( a₂ - a₁) · ( b₁ × b₂) |.

Question 95

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Read the two statements and choose the correct option.
I. Two lines with direction cosines $l_1, m_1, n_1$ and $l_2, m_2, n_2$ are perpendicular exactly when $l_1l_2 + m_1m_2 + n_1n_2 = 0$ .
II. The shortest distance between skew lines is $\lvert (\vec{a_2} - \vec{a_1}) \cdot (\vec{b_1} \times \vec{b_2}) \rvert$ .

Only ICorrect answerYour answerOnly IICorrect answerYour answerBoth I and IICorrect answerYour answerNeither I nor IICorrect answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

I: $\cos \theta = l_1l_2 + m_1m_2 + n_1n_2$ , which is 0 for $90^\circ$ . True.
II: it must still be divided by $\lvert \vec{b_1} \times \vec{b_2} \rvert$ . False.

Ten questions from Three-Dimensional Geometry, at your own pace.