What is the cross product of $[1, 4, - 2]$ $[1, 4, -2]$ and $[3, 0, 5]$ $[3, 0, 5]$ ?

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Answer 1 · 2017-01-18T15:41:33

$20 ˆ \to i - 11 ˆ \to j - 12 ˆ \to k$ $20hatveci-11hatvecj-12hatveck$

the cross product of two vectors

$\to a = [a_{1}, a_{2}, a_{3}]$ $veca=[a_1,a_2,a_3]$ and $\to b = [b_{1}, b_{2}, b_{3}]$ $vecb=[b_1,b_2,b_3]$

is calculated by the determinate

$vecaxxvecb=|(hatveci,hatvecj,hatveck),(a_1,a_2,a_3),(b_1,b_2,b_3)|$

so we have here

$vecaxxvecb=|(hatveci,hatvecj,hatveck),(1,4,-2),(3,0,5)|$

expanding by Row 1

$=hatveci|(4,-2),(0,5)|-hatvecj|(1,-2),(3,5)|+hatveck|(1,4),(3,0)|$

$=(4xx5-0xx(-2))hatveci-(1xx5-3xx(-2))hatvecj+(1xx0-4xx3)hatveck$

$=20hatveci-11hatvecj-12hatveck$

What is the cross product of [1, 4, -2][1,4,−2][1, 4, -2] and [3, 0, 5] [3,0,5][3, 0, 5] ?