jelentetvq

2022-01-24

How do I find the unit vector for $v=<2,-5,6>$

chaloideq1

Expert

A unit vector just means a vector whose length equals 1 unit. We want a unit vector u in the v -direction. We will use $u=\frac{v}{|v|}$.
Note: Any vector parallel to v can be written as c v with real c; if $c>0$ this goes in the same direction as v.
The length |v| of a vector $v=$ is
$|v|=\sqrt{{x}^{2}+{y}^{2}+{z}^{2}}$, and so
$|<2,-5,6>|=\sqrt{{2}^{2}+{\left(-5\right)}^{2}+{6}^{2}}$
$=\sqrt{4+25+36}=\sqrt{65}$
we can divide v by $\sqrt{65}$ to get
$u=<\frac{2}{\sqrt{65}},\frac{-5}{\sqrt{65}},\frac{6}{\sqrt{65}}>$

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