What is the cross product of $(4 i + 4 j + 2 k)$ $(4 i + 4 j + 2 k)$ and $(i + j - 7 k)$ $(i + j -7k)$ ?

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Answer 1 · 2016-12-18T18:26:07

The vector is $= ⟨ - 30, 30, 0 ⟩$ $=〈-30,30,0〉$

The cross product is obtained from the determinant

$| (hati,hatj,hatk), (4,4,2), (1,1,-7) |$

$=hati(-28-2)-hatj(-28-2)+hatk(0)$

$=〈-30,30,0〉$

Verification

we do a dot product

$〈-30,30,0〉.〈4,4,2〉=(-120+120+0=0)$

$〈-30,30,0〉.〈1,1,-7〉=(-30+30-0)=0$

What is the cross product of (4 i + 4 j + 2 k)(4i+4j+2k)(4 i + 4 j + 2 k) and (i + j -7k)(i+j−7k)(i + j -7k)?