What is the cross product of $<7, 5 ,6 >$ and $<3 ,5 ,-6 >$ ?

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Answer 1 · 2017-01-05T11:32:43

The answer is $=〈-60,60,20〉$

The cross product of 2 vectors, $〈a,b,c〉$ and $d,e,f〉$

is given by the determinant

$| (hati,hatj,hatk), (a,b,c), (d,e,f) |$

and $| (a,b), (c,d) |=ad-bc$

Here, the 2 vectors are $〈7,5,6〉$ and $〈3,5,-6〉$

And the cross product is

$| (hati,hatj,hatk), (7,5,6), (3,5,-6) |$

$=hati| (5,6), (5,-6) | - hatj| (7,6), (3,-6) |+hatk | (7,5), (3,5) |$

$=hati(-30-30)-hati(-42-18)+hatk(35-15)$

$=〈-60,60,20〉$

Verification, by doing the dot product

$〈-60,60,20〉.〈7,5,6〉=-420+300+120=0$

$〈-60,60,20〉.〈3,5,-6〉=-180+300-120=0$

Therefore, the vector is perpendicular to the other 2 vectors

What is the cross product of <7, 5 ,6 ><7, 5 ,6 > and <3 ,5 ,-6 ><3 ,5 ,-6 >?