# What is the cross product of [2, 1, -4] and [2, 5, 4] ?

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#### Explanation:

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1
Sep 14, 2016

$24 \hat{i} - 16 \hat{j} + 8 \hat{k}$ is the answer.

#### Explanation:

Let $\vec{A} = \left[2 , 1 , - 4\right]$ and $\vec{B} = \left[2 , 5 , 4\right]$

So,$\left[{a}_{1} , {a}_{2} , {a}_{3}\right]$ is $\left[2 , 1 , - 4\right]$

and $\left[{b}_{1} , {b}_{2} , {b}_{3}\right]$ is $\left[2 , 5 , 4\right]$

$\vec{A}$ x $\vec{B}$ = $\hat{i} \left({a}_{2} {b}_{3} - {a}_{3} {b}_{2}\right) - \hat{j} \left({a}_{1} {b}_{3} - {a}_{3} {b}_{1}\right) + \hat{k} \left({a}_{1} {b}_{2} - {a}_{2} {b}_{1}\right)$.............(I have not written it in determinant form as I don't know how to represent it here.)

$\vec{A}$ x $\vec{B}$ = $\hat{i} \left(4 + 20\right) - \hat{j} \left(8 + 8\right) + \hat{k} \left(10 - 2\right) = 24 \hat{i} - 16 \hat{j} + 8 \hat{k}$

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