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

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Answer 1 · 2016-10-29T03:21:59

$<27, -20, 5>$

Convert to $hati, hatj, hatk$ notation

$barA = 5hati + 5hatj - 7hatk$
$barB = 5hati + 6hatj - 3hatk$

The cross product can be computed using a determinant:

$barA xx barB = | (hati, hatj, hatk, hati, hatj), (5, 5, - 7,5, 5), (5, 6, -3, 5, 6) | =$

${(5)(-3)-(-7)(6)}hati + {(-7)(5) - (5)(-3)}hatj + {(5)(6) - (5)(5)}hatk =$

$27hati - 20hatj + 5hatk$

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