A line L₁ makes equal acute angles with the coordinate axes, and a line L₂ has direction ratios 6, -2, 3. What is the cosine of the angle between L₁ and L₂?

Question 79

MediumOriginal question

A line $L_1$ makes equal acute angles with the coordinate axes, and a line $L_2$ has direction ratios $6, -2, 3$ . What is the cosine of the angle between $L_1$ and $L_2$ ?

\frac{1}{3}

Correct answerYour answer

\frac{\sqrt{3}}{3}

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\frac{11 \sqrt{3}}{21}

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1

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

$L_1$ has direction ratios $1, 1, 1$ , of length $\sqrt{3}$ ; $L_2$ has length $\sqrt{36 + 4 + 9} = 7$ .
$\cos \theta = \frac{\lvert 6 - 2 + 3 \rvert}{7\sqrt{3}} = \frac{1}{\sqrt{3}} = \frac{\sqrt{3}}{3}$ .

Worth noting

$\frac{1}{3}$ takes each direction cosine of $L_1$ as $\frac{1}{3}$ instead of $\frac{1}{\sqrt{3}}$ .

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