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

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Answer 1 · 2016-12-07T17:43:31

The answer is $= ⟨ - 31, - 14, - 1 ⟩$ $=〈-31,-14,-1〉$

The cross product of 2 vectors

$\to a = ⟨ a_{1}, a_{2}, a_{3} ⟩$ $veca=〈a_1,a_2,a_3〉$

and $\to b = ⟨ b_{1}, b_{2} b_{3} ⟩$ $vecb=〈b_1,b_2b_3〉$

is given by

the determinant $| (hati,hatj,hatk), (a_1,a_2,a_3), (b_1,b_2,b_3) |$

$=hati(a_2b_3-a_3b_2)-hatj(a_1b_3-a_3b_1)+hatk(a_1b_2-a_2b_1)$

Here we have,

$〈1.-2-3〉$ and $〈2,-5,8〉$

So, the cross product is

$| (hati,hatj,hatk), (1,-2,-3), (2,-5,8) |$

$=hati(-16-15)-hatj(8+6)+hatk(-5+4)$

$=〈-31,-14,-1〉$

Verification (the dot product of perpendicular vectors is $=0$ )

$〈-31,-14,-1〉.〈1.-2-3〉=-31+28+3=0$

$〈-31,-14,-1〉.〈2,-5,8〉=-62+70-8=0$

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