What is the cross product of $(- 5 i + 4 j - 5 k)$ $(- 5 i + 4 j - 5 k)$ and $(i + j - 7 k)$ $(i + j -7k)$ ?

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Answer 1 · 2016-07-03T21:01:19

$= - 23 ˆ i - 40 ˆ j - 9 ˆ k$ $= -23 hat i -40 hat j -9 hat k$

the cross product is the determinant of this matrix

$[(hat i, hat j,hat k), (-5, 4, -5), (1,1,-7)]$

which is

$hat i [(4)(-7)-(1)(-5)]$

$- hat j [(-5)(-7) - (1)(-5)]$

$+ hat k [(-5)(1) - (1)(4)]$

$= [(-23), (-40), (-9)]$

What is the cross product of (- 5 i + 4 j - 5 k)(−5i+4j−5k)(- 5 i + 4 j - 5 k) and (i + j -7k)(i+j−7k)(i + j -7k)?