What is the cross product of $<-1, 2 ,27 >$ and $<-3 ,1 ,-1 >$ ?

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Answer 1 · 2016-12-29T06:30:14

The answer is $=〈-29,-82,5〉$

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 $〈-1,2,27〉$ and $〈-3,1,-1〉$

And the cross product is

$| (hati,hatj,hatk), (-1,2,27), (-3,1,-1) |$

$=hati| (2,27), (1,-1) | - hatj| (-1,27), (-3,-1) |+hatk | (-1,2), (-3,1) |$

$=hati(-2-27)-hati(1+81)+hatk(-1+6)$

$=〈-29,-82,5〉$

Verification, by doing the dot product

$〈-29,-82,5〉.〈-1,2,27〉=29-164+135=0$

$〈-29,-82,5〉.〈-3,1,-1〉=87-82-5=0$

Therefore, the vector is perpendicular to the other 2 vectors

What is the cross product of <-1, 2 ,27 ><-1, 2 ,27 > and <-3 ,1 ,-1 ><-3 ,1 ,-1 >?