How do you find a unit vector in the direction of 3i+4j-k?

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Answer 1 · 2016-09-18T08:53:47

$(3 i + 4 j - k) / (sqrt(26))$

We have: $3 i + 4 j - k$

Let $u = 3 i + 4 j - k$ .

Unit vectors are of the form $hat(u) = (u) / (abs(u))$ :

$=> hat(u) = (3 i + 4 j - k) / (abs(3 i + 4 j - k))$

$=> hat(u) = (3 i + 4 j - k) / (sqrt(3^(2) + 4^(2) + (- 1)^(2)))$

$=> hat(u) = (3 i + 4 j - k) / (sqrt(9 + 16 + 1))$

$=> hat(u) = (3 i + 4 j - k) / (sqrt(26))$