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How do you find the unit vector in the same direction as (-5, 3)?

1 Answer

Aug 13, 2017

Given a vector $\to v = (a, b)$ $vecv = (a,b)$ ; the unit vector is:

$ˆ v = \frac{\to v}{∣ ∣ \to v ∣ ∣}$ $hatv = vecv/|vecv|$

Where $∣ ∣ \to v ∣ ∣ = \sqrt{a^{2} + b^{2}}$ $|vecv| = sqrt(a^2+b^2)$

Explanation:

Given: $\to v = (- 5, 3)$ $vecv = (-5,3)$

$ˆ v = \frac{(- 5, 3)}{\sqrt{{(- 5)}^{2} + 3^{2}}}$ $hatv = ("("-5,3")")/sqrt((-5)^2+3^2)$

$ˆ v = \frac{(- 5, 3)}{\sqrt{34}}$ $hatv = ("("-5,3")")/sqrt(34)$

$ˆ v = (- \frac{5}{\sqrt{34}}, \frac{3}{\sqrt{34}})$ $hatv = (-5/sqrt(34),3/sqrt(34))$

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