What is the unit vector of this vector v = -2i + 5j?

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What is the unit vector of this vector v = -2i + 5j?

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Answer 1 · 2016-07-15T10:40:46

$\to u = - \frac{2}{\sqrt{29}} i + \frac{5}{\sqrt{29}} j$ $color(blue)(vec(u)=-2/sqrt(29)i+5/sqrt(29)j)$ is a unit vector with the same direction as $\to v = - 2 + 5 j$ $vec(v)=-2+5j$

Explanation:

The unit vector, $\to u$ $vec(u)$ corresponding to a given vector $\to v$ $vec(v)$ can be calculated by dividing the terms of $\to v$ $vec(v)$ by the magnitude (length) of $\to v$ $vec(v)$

$XXX \to u = \frac{\to v}{∣ ∣ \to v ∣ ∣}$ $color(white)("XXX")vec(u)=vec(v)/abs(vec(v))$

$∣ ∣ \to v ∣ ∣$ $abs(vec(v))$ is calculated using the Pythagorean Theorem.
In this case with $\to v = - 2 i + 5 j$ $vec(v)=-2i+5j$
$XXX ∣ ∣ \to v ∣ ∣ = \sqrt{{(- 2)}^{2} + 5^{2}} = \sqrt{29}$ $color(white)("XXX")abs(vec(v))=sqrt((-2)^2+5^2)=sqrt(29)$

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What is the unit vector of this vector v = -2i + 5j?

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