What is the angle between 3 i - 4 k and 2 i + 2 j - k?

Question 84

MediumOriginal question

What is the angle between $3\hat{i} - 4\hat{k}$ and $2\hat{i} + 2\hat{j} - \hat{k}$ ?

\cos^{-1}\frac{2}{15}

Correct answerYour answer

\cos^{-1}\frac{2}{5}

Correct answerYour answer

\cos^{-1}\frac{2}{3}

Correct answerYour answer

\sin^{-1}\frac{2}{3}

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

$\vec{a} \cdot \vec{b} = 3(2) + 0(2) + (-4)(-1) = 10$ , $\lvert \vec{a} \rvert = 5$ and $\lvert \vec{b} \rvert = 3$ .
$\cos \theta = \frac{10}{15} = \frac{2}{3}$ , so $\theta = \cos^{-1}\frac{2}{3}$ .

Worth noting

$\cos^{-1}\frac{2}{15}$ takes $(-4)(-1)$ as $-4$ , so the scalar product comes out as 2.

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