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

$\frac{3 i + 4 j - k}{\sqrt{26}}$ $(3 i + 4 j - k) / (sqrt(26))$

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

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

Unit vectors are of the form $ˆ u = \frac{u}{| u |}$ $hat(u) = (u) / (abs(u))$ :

$\Rightarrow ˆ u = \frac{3 i + 4 j - k}{| 3 i + 4 j - k |}$ $=> hat(u) = (3 i + 4 j - k) / (abs(3 i + 4 j - k))$

$\Rightarrow ˆ u = \frac{3 i + 4 j - k}{\sqrt{3^{2} + 4^{2} + {(- 1)}^{2}}}$ $=> hat(u) = (3 i + 4 j - k) / (sqrt(3^(2) + 4^(2) + (- 1)^(2)))$

$\Rightarrow ˆ u = \frac{3 i + 4 j - k}{\sqrt{9 + 16 + 1}}$ $=> hat(u) = (3 i + 4 j - k) / (sqrt(9 + 16 + 1))$

$\Rightarrow ˆ u = \frac{3 i + 4 j - k}{\sqrt{26}}$ $=> hat(u) = (3 i + 4 j - k) / (sqrt(26))$