# Chapter 9 - Polar Coordinates; Vectors - 9.7 The Cross Product - 9.7 Assess Your Understanding - Page 632: 59

We know that if $u$ and $v$ are orthogonal, their included angle is $\theta=90^\circ$. Thus, $||u\times v||=||u||\ ||v||\sin{\theta}=||u||\ ||v||\sin{90^\circ}=||u||\ ||v||(1)=||u||\ ||v||.$ If $u$ and $v$ are unit vectors, then $||u||=||v||=1$. Thus, $||u\times v||=||u||\ ||v||=(1)(1)=1$, so it must also be a unit vector, because its magnitude is $1$.

#### Work Step by Step

We know that if $u$ and $v$ are orthogonal, their included angle is $\theta=90^\circ$. Thus, $||u\times v||=||u||\ ||v||\sin{\theta}=||u||\ ||v||\sin{90^\circ}=||u||\ ||v||(1)=||u||\ ||v||.$ If $u$ and $v$ are unit vectors, then $||u||=||v||=1$. Thus, $||u\times v||=||u||\ ||v||=(1)(1)=1$, so it must also be a unit vector, because its magnitude is $1$.

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