Question

Cross product of `(2 hat i + 3 hat j) xx (5 hat i + hat j)` ?

Answer 1

`-13hatk`

Explanation:

Following the rule of vector cross,i.e

`hati×hat i`= `hatj×hat j=0`

and, `hat i ×hat j=hat k` and, `hat j×hat i=-hatk`

So,`(2hati+3hatj)×(5hati+hatj)=(2hati×hatj+3hatj×5hati)=2hatk-15hatk=-13hatk`

Answer 2

The vector is `= <0,0,-13>`

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=〈2,3,0〉` and `vecb=〈5,1,0〉`

Therefore,

`| (veci,vecj,veck), (2,3,0), (5,1,0) |`

`=veci| (3,0), (1,0) | -vecj| (2,0), (5,0) | +veck| (2,3), (5,1) |`

`=veci((3)*(0)-(1)*(0))-vecj((2)*(0)-(5)*(0))+veck((2)*(1)-(3)*(5))`

`=〈0,0,-13〉=vecc`

Verification by doing 2 dot products

`〈0,0,-13〉.〈2,3,0〉=(0)*(2)+(0)*(3)+(-13)*(0)=0`

`〈0,0,-13〉.〈5,1,0〉=(0)*(5)+(0)*(1)+(-13)*(0)=0`

So,

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