What is the cross product of <-3,5,8 ><−3,5,8> and <6, -2, 7 ><6,−2,7>?

2 Answers
Narad T.
Apr 22, 2017

The vector is =〈51,69,-24〉==⟨51,69,−24⟩=

Explanation:

The cross product of 2 vectors is calculated with the determinant

| (veci,vecj,veck), (d,e,f), (g,h,i) |

where 〈d,e,f〉 and 〈g,h,i〉 are the 2 vectors

Here, we have veca=〈-3,5,8〉 and vecb=〈6,-2,7〉

Therefore,

| (veci,vecj,veck), (-3,5,8), (6,-2,7) |

=veci| (5,8), (-2,7) | -vecj| (-3,8), (6,7) | +veck| (-3,5), (6,-2) |

=veci(5*7+2*8)-vecj(-3*7-6*8)+veck(3*2-5*6)

=〈51,69,-24〉=vecc

Verification by doing 2 dot products

〈51,69,-24〉.〈-3,5,8〉=-51*3+69*5-24*8=0

〈51,69,-24〉.〈6,-2,7〉=51*6-69*2-24*7=0

So,

vecc is perpendicular to veca and vecb

Ratnaker Mehta
Apr 22, 2017

=(51,69,-24).

Explanation:

Let, vecx=(-3,5,8)=-3i+5j+8k, and,

vecy=(6,-2,7)=6i-2j+7k.

:. vecx xx vecy=|(i,j,k),(-3,5,8),(6,-2,7)|

=(35-(-16))i-(-21-48)j+(6-30)k

=51i+69j-24k

=(51,69,-24).

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