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Calculate $\|\boldsymbol{c}\|$ if $\mathbf c= 2\boldsymbol{a} \times \boldsymbol{b}$ and $\boldsymbol{a} = 3\hat{\boldsymbol{k}} - 2\hat{\boldsymbol{j}}$ and $\boldsymbol{b} = 3\hat{\boldsymbol{i}} - 2\hat{\boldsymbol{j}}$.

Can't find vectors length.

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  • $\begingroup$ Can't you write the borders using mathjax? $\endgroup$
    – AHB
    Nov 19, 2015 at 15:44
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    $\begingroup$ Do you know how to compute the cross product? $\endgroup$
    – Rocket Man
    Nov 19, 2015 at 15:44
  • $\begingroup$ tag algebraic-geometry doesn't seem suitable for this problem $\endgroup$
    – Mirko
    Nov 19, 2015 at 15:50
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    $\begingroup$ @Nenq Here's a little overview of how to use MathJax. To get $|x|$ type $|x|$. To get $\|x\|$ type $\|x\|$. To get $\vec c = 2\vec a \times \vec b$ type $\vec c = 2\vec a \times \vec b$. In the future try to format your questions using this so that it's easier for us to read. $\endgroup$
    – user137731
    Nov 19, 2015 at 15:51
  • $\begingroup$ Thanks, sorry I am new here. $\endgroup$
    – Nenq
    Nov 19, 2015 at 15:55

2 Answers 2

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So we have:

$$c = 2\overrightarrow{a} \times \overrightarrow{b} $$

$$=2\det \begin{pmatrix}i & j & k \\ 0 & -2& 3 \\ 3 & -2 & 0\end{pmatrix}$$

$$=2\begin{pmatrix} 6 \\ 9 \\ 6 \end{pmatrix}$$

$$=\begin{pmatrix} 12 \\ 18 \\ 12 \end{pmatrix}$$

where I used the cofactor expansion about the first row to take the determinant and now the length is given as:

$$\|c\| = \sqrt{12^2 + 18^2 + 12^2}$$

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  • $\begingroup$ I am so stupid, i thought that "x" was missing variable, not multiplication sign. :D $\endgroup$
    – Nenq
    Nov 19, 2015 at 15:51
  • $\begingroup$ I would say that if you see two vectors on both sides of the "x", assume that it is a cross product. $\endgroup$ Nov 19, 2015 at 15:52
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Ya so we start the vectors are $6k-4j$ and $3i-2j$ so we need to take cross product which is given by determinant form . I hope that you know that basics of vectors so we get $c=18j+12k$ thus its mod is $2\sqrt{117}$ . Please share your effort next time as you are new here.

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