What is the cross product of $<5, 2 ,5 >$ and $<4 ,1 ,9 >$ ?

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Answer 1 · 2016-07-04T20:12:08

$< 5, 2, 5 > xx < 4, 1, 9 > = < 13, -25, -3 >$

The cross product of two $3$ dimensional vectors can be defined by the formula:

$< u_1, u_2, u_3 > xx < v_1, v_2, v_3 > = < abs((u_2, u_3),(v_2, v_3)), abs((u_3, u_1),(v_3, v_1)), abs((u_1,u_2),(v_1,v_2))>$

In our example we find:

$< 5, 2, 5 > xx < 4, 1, 9 >$

$= < abs((2,5),(1,9)), abs((5,5),(9,4)), abs((5,2),(4,1)) >$

$= < (18-5), (20-45), (5-8) >$

$= < 13, -25, -3 >$

What is the cross product of <5, 2 ,5 ><5, 2 ,5 > and <4 ,1 ,9 ><4 ,1 ,9 >?