# Chapter 5 - Inner Product Spaces - 5.1 Length and Dot Product in Rn - 5.1 Exercises: 11

a) $=(\frac{3}{\sqrt {38}},\frac{2}{\sqrt {38}}, -\frac{5}{\sqrt {38}})$ b) $=(-\frac{3}{\sqrt {38}},-\frac{2}{\sqrt {38}}, \frac{5}{\sqrt {38}})$

#### Work Step by Step

a) The magnitude of this vector is given by $\sqrt {(3)^{2} +(2)^{2}+(-5)^{2}}=\sqrt {38}$. Therefore a unit vector in direction $u$ is given by: $\frac{1}{\sqrt {38}}(3,2,-5)$ $=(\frac{3}{\sqrt {38}},\frac{2}{\sqrt {38}}, -\frac{5}{\sqrt {38}})$ b) a unit vector in the opposite direction is given by multiplying the unit vector found in part a) by $(-1)$ This is equal to $(-1)\times(\frac{3}{\sqrt {38}},\frac{2}{\sqrt {38}}, -\frac{5}{\sqrt {38}})$ $=(-\frac{3}{\sqrt {38}},-\frac{2}{\sqrt {38}}, \frac{5}{\sqrt {38}})$

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