a = 4 i - 4 j + 2 k. For which values of λ is λ a a unit vector?

Question 19

MediumOriginal question

$\vec{a} = 4\hat{i} - 4\hat{j} + 2\hat{k}$ . For which values of $\lambda$ is $\lambda\vec{a}$ a unit vector?

\lambda = \pm\frac{1}{6}

Correct answerYour answer

\lambda = \frac{1}{6}

Correct answerYour answer

\lambda = \pm\frac{1}{36}

Correct answerYour answer

\lambda = \pm 6

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

$\lvert \vec{a} \rvert = \sqrt{16 + 16 + 4} = 6$ , and $\lvert \lambda\vec{a} \rvert = \lvert \lambda \rvert \lvert \vec{a} \rvert = 6\lvert \lambda \rvert$ .
$6\lvert \lambda \rvert = 1$ gives $\lambda = \pm\frac{1}{6}$ .

Worth noting

$\frac{1}{6}$ alone misses the negative value: $-\frac{1}{6}\vec{a}$ also has magnitude 1.

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