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If r=xi+yj+zk ,find (r x i).( r x j)+xy - Mathematics

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If `vecr=xhati+yhatj+zhatk` ,find `(vecrxxhati).(vecrxxhatj)+xy`

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Solution

Given

`vecr=xhati+yhatj+zhatk`

`(vecrxxhati).(vecrxxhatj)+xy`

`=[(xhati+yhatj+zhatk)xxhati].[(xhati+yhatj+zhatk)xxhatj]+xy`

`=[(xhatixxhati+yhatjxxhati+zhatkxxhati)].[(xhatixxhatj+yhatjxxhatj+zhatkxxhatj)]+xy`

`=(0hati-yhatk+zhatj).(xhatk+0hatj-zhati)+xy`

`=(0z-xy+0z)+xy`

`=-xy+xy`

`=0`

Concept: Vectors Examples and Solutions
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