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How do you find the unit vector for v = -6i +5j?

1 Answer

Dec 15, 2016

$ˆ \to v = \frac{\sqrt{61}}{61} (- 6 \to i + 5 \to j)$ $hatvecv=sqrt61/61(-6veci+5vecj)$

Explanation:

unit vector is defined as

$ˆ \to a = \frac{\to a}{∣ ∣ \to a ∣ ∣}$ $hatveca=veca/|veca|$

$\to v = - 6 \to i + 5 \to j$ $vecv=-6veci+5vecj$

$∣ ∣ \to v ∣ ∣ = \sqrt{6^{2} + 5^{2}} = \sqrt{36 + 25} = \sqrt{61}$ $|vecv|=sqrt(6^2+5^2)=sqrt(36+25)=sqrt61$

$ˆ \to v = \frac{1}{\sqrt{61}} (- 6 \to i + 5 \to j)$ $hatvecv=1/sqrt61(-6veci+5vecj)$

$ˆ \to v = \frac{\sqrt{61}}{61} (- 6 \to i + 5 \to j)$ $hatvecv=sqrt61/61(-6veci+5vecj)$

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