# Chapter 12 - Section 12.4 - The Cross Product - 12.4 Exercises - Page 821: 19

$\lt (\frac{-1}{3\sqrt 3}),(\frac{-1}{3\sqrt 3}),(\frac{5}{3\sqrt 3}) \gt$ and $\lt (\frac{1}{3\sqrt 3}),(\frac{1}{3\sqrt 3}),(\frac{-5}{3\sqrt 3}) \gt$

#### Work Step by Step

$\begin{vmatrix} i&j&k \\ 3& 2&1\\-1&1&0\end{vmatrix}= \lt -1,-1,5 \gt$ $d=\sqrt {(-1)^2+(-1)^2+(5)^2}$ $=\sqrt {27}$ $=3\sqrt 3$ $=\lt -1,-1,5 \gt \div 3\sqrt 3$ $=\lt (\frac{-1}{3\sqrt 3}),(\frac{-1}{3\sqrt 3}),(\frac{5}{3\sqrt 3}) \gt$ $\begin{vmatrix} i&j&k \\ -1&1&0\\ 3& 2&1 \end{vmatrix}= \lt 1,1,-5 \gt$ $d=\sqrt {(1)^2+(1)^2+(-5)^2}$ $=\sqrt {27}$ $=3\sqrt 3$ $=\lt 1,1,-5 \gt \div 3\sqrt 3$ $=\lt (\frac{1}{3\sqrt 3}),(\frac{1}{3\sqrt 3}),(\frac{-5}{3\sqrt 3}) \gt$

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