What is the cross product of $[1, - 3, 2]$ $[1, -3, 2]$ and $[- 8, 5, 1]$ $[-8, 5, 1]$ ?

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Answer 1 · 2016-04-29T23:26:45

Cross product is a vector
$- 13 i - 17 j - 19 k$ $-13i-17j-19k$

Let vector $a = 1 \cdot i - 3 \cdot j + 2 \cdot k$ $a=1*i-3*j+2*k$ and $b = - 8 \cdot i + 5 \cdot j + 1 \cdot k$ $b=-8*i+5*j+1*k$

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 $b=[(i,j,k),(1,-3,2),(-8,5,1)]$

$a$ x $b=$

$+(-3)(1)i+(2)*(-8)j+(1)(5)k-(-3)(-8)k-(2)(5)i-(1)(1)j$

$a$ x $b=-3i-10i-16j-j+5k-24k$

$a$ x $b=-13i-17j-19k$

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

What is the cross product of [1, -3, 2][1,−3,2][1, -3, 2] and [-8, 5, 1] [−8,5,1][-8, 5, 1] ?