KEAM Unit Vector — practice questions

Explore 2 free Unit Vector questions in KEAM Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Unit Vector questions and exercises with answers

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A unit vector along a non-zero vector $\vec a$ is given by:Read the answer and worked solution →Find a unit vector in the direction of $\vec a = \hat i - 2\hat j$:Read the answer and worked solution →

Worked practice questions

A unit vector along a non-zero vector $\vec a$ is given by:

$\vec a / |\vec a|$
$|\vec a| \cdot \vec a$
$\vec a / 2$
$2\vec a / |\vec a|^2$

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Correct answer: A. $\vec a / |\vec a|$

$\hat a = \vec a / |\vec a|$ — divide a vector by its magnitude to get a unit vector in the same direction. It always has magnitude 1.

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Find a unit vector in the direction of $\vec a = \hat i - 2\hat j$:

$\hat i - 2\hat j$
$(\hat i - 2\hat j)/\sqrt 5$
$(\hat i - 2\hat j)/5$
$(\hat i - 2\hat j)/3$

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Correct answer: B. $(\hat i - 2\hat j)/\sqrt 5$

$|\vec a| = \sqrt{1^2 + 2^2} = \sqrt 5$. Unit vector $\hat a = \vec a / |\vec a| = (\hat i - 2\hat j)/\sqrt 5$.