How do you find the unit vector in the direction of the given vector of $v = i + j$ $v=i+j$ ?

Question

9654 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-01-11T13:54:27

$ˆ \to v = \frac{\sqrt{2}}{2} (ˆ \to i + ˆ \to j)$ $hatvecv=sqrt2/2(hatveci+hatvecj)$

By definition a unit vector has a magnitude (modulus) of 1. So to find a unit vector of any given vector in that direction we work out:

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

in this case

$\to v = ˆ \to i + ˆ \to j$ $vecv=hatveci+hatvecj$

$∣ ∣ \to v ∣ ∣ = \sqrt{1^{2} + 1^{2}} = \sqrt{2}$ $|vecv|=sqrt(1^2+1^2)=sqrt2$

$ˆ \to v = \frac{1}{\sqrt{2}} (ˆ \to i + ˆ \to j)$ $hatvecv=1/sqrt2(hatveci+hatvecj)$

$ˆ \to v = \frac{\sqrt{2}}{2} (ˆ \to i + ˆ \to j)$ $hatvecv=sqrt2/2(hatveci+hatvecj)$

How do you find the unit vector in the direction of the given vector of v=i+jv=i+j?