Question

What is the cross product of `(2i -3j + 4k)` and `(i + j -7k)`?

Answer 1

`17i+18j+5k`

Explanation:

The cross-product of vectors `(2i-3j+4k)` & `(i+j-7k)` is given by using determinant method

`(2i-3j+4k)\times(i+j-7k)=17i+18j+5k`

Answer 2

The vector is `= 〈17,18,5〉`

Explanation:

The cross product of 2 vectors is calculated with the determinant

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

where `veca=〈d,e,f〉` and `vecb=〈g,h,i〉` are the 2 vectors

Here, we have `veca=〈2,-3,4〉` and `vecb=〈1,1,-7〉`

Therefore,

`| (veci,vecj,veck), (2,-3,4), (1,1,-7) |`

`=veci| (-3,4), (1,-7) | -vecj| (2,4), (1,-7) | +veck| (2,-3), (1,1) |`

`=veci((-3)*(-7)-(4)*(1))-vecj((2)*(-7)-(4)*(1))+veck((2)*(1)-(-3)*(1))`

`=〈17,18,5〉=vecc`

Verification by doing 2 dot products

`〈17,18,5〉.〈2,-3,4〉=(17)*(2)+(18)*(-3)+(5)*(4)=0`

`〈17,18,5〉.〈1,1,-7〉=(17)*(1)+(18)*(1)+(5)*(-7)=0`

So,

`vecc` is perpendicular to `veca` and `vecb`