What is the cross product of $[2, - 1, 2]$ $[2,-1,2]$ and $[4, - 3, 1]$ $[4,-3,1]$ ?

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Answer 1 · 2016-04-30T02:28:10

the cross product
$a$ $a$ x $b = + 5 i + 6 j - 2 k$ $b=+5i+6j-2k$

Let vector $a = 2 \cdot i - 1 \cdot j + 2 \cdot k$ $a=2*i-1*j+2*k$ and $b = 4 \cdot i - 3 \cdot j + 1 \cdot k$ $b=4*i-3*j+1*k$

The formula for cross product

$a$ $a$ x $b=[(i,j,k),(a_1,a_2,a_3),(b_1,b_2,b_3)]$

$a$ x $b=+a_2b_3i+a_3b_1j+a_1b_2k-a_2b_1k-a_3b_2i-a_1b_3j$

Let us solve the cross product

$a$ x $b=[(i,j,k),(2,-1,2),(4,-3,1)]$

$a$ x $b=$

$+(-1)(1)i+(2)(4)j+(2)(-3)k-(-1)(4)k-(2)(-3)i-(2)(1)j$

$a$ x $b=-1*i+6i+8j-2j-6k+4k$

$a$ x $b=+5i+6j-2k$

God bless...I hope the explanation is useful.

What is the cross product of [2,-1,2][2,−1,2][2,-1,2] and [4,-3,1] [4,−3,1][4,-3,1] ?