What is the cosine of the angle between the lines with direction cosines $\frac{2}{7}, \frac{3}{7}, \frac{6}{7}$ and $\frac{6}{7}, -\frac{2}{7}, \frac{3}{7}$ ?

\frac{6}{49}

Correct answerYour answer

\frac{12}{49}

Correct answerYour answer

\frac{24}{49}

Correct answerYour answer

\frac{36}{49}

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

With direction cosines, $\cos \theta = \lvert l_1l_2 + m_1m_2 + n_1n_2 \rvert$ : there is nothing to divide by.
$\frac{12 - 6 + 18}{49} = \frac{24}{49}$ .

Worth noting

$\frac{36}{49}$ drops the minus sign of $-\frac{2}{7}$ .

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

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

What is the cosine of the angle between the lines with direction cosines 27,37,67\frac{2}{7}, \frac{3}{7}, \frac{6}{7}72​,73​,76​ and 67,−27,37\frac{6}{7}, -\frac{2}{7}, \frac{3}{7}76​,−72​,73​?