What is cos A, the cosine of the angle at A?

Question 105

MediumOriginal question

A triangle has vertices $A(1, 1, 1)$ , $B(2, 3, 3)$ and $C(3, 1, 2)$ .

What is $\cos A$ , the cosine of the angle at $A$ ?

\frac{2 \sqrt{5}}{15}

Correct answerYour answer

\frac{4}{9}

Correct answerYour answer

\frac{4 \sqrt{5}}{15}

Correct answerYour answer

\frac{4}{5}

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

$\lvert \overrightarrow{AB} \rvert = 3$ and $\lvert \overrightarrow{AC} \rvert = \sqrt{5}$ .
$\cos A = \frac{4}{3\sqrt{5}} = \frac{4 \sqrt{5}}{15}$ .

Worth noting

$\frac{4}{9}$ divides by $\lvert \overrightarrow{AB} \rvert^{2}$ instead of the product of the two magnitudes.

Ten questions from Vectors, at your own pace.

Ten questions from Vectors, at your own pace.