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

Question

1351 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-10-29T03:21:59

$< 27, - 20, 5 >$ $<27, -20, 5>$

Convert to $ˆ i, ˆ j, ˆ k$ $hati, hatj, hatk$ notation

$¯ ¯ ¯ A = 5 ˆ i + 5 ˆ j - 7 ˆ k$ $barA = 5hati + 5hatj - 7hatk$
$¯ ¯ ¯ B = 5 ˆ i + 6 ˆ j - 3 ˆ k$ $barB = 5hati + 6hatj - 3hatk$

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><5 , 5 ,-7 > and <5 ,6 ,-3 ><5,6,−3><5 ,6 ,-3 >?