What is the cross product of $[3, 1, - 4]$ $[3, 1, -4]$ and $[2, 6, - 1]$ $[2, 6, -1]$ ?

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Answer 1 · 2016-08-24T08:57:39

$= 23 ˆ x - 5 ˆ y + 16 ˆ z$ $= 23 hat x -5 hat y + 16 hat z$

the cross product you seek is the determinant of the following matrix

$((hat x, hat y , hat z),(3,1,-4),(2,6,-1))$

$= hat x(1*(-1) - (-4)*6) - hat y (3 * (-1) - (-4)*2) + hat z (3*6 - 2*1)$

$= 23 hat x -5 hat y + 16 hat z$

this should be perpendicular to these 2 vectors and we can check that via the scalar dot product

$<23 , -5 , 16 >* <3,1,-4> = 69 - 5 - 64 = 0$

$<23 , -5 , 16 >* <2,6,-1> = 46 - 30 -16 = 0$

What is the cross product of [3, 1, -4][3,1,−4][3, 1, -4] and [2, 6, -1] [2,6,−1][2, 6, -1] ?