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What inference can you draw if vec axx ...

What inference can you draw if ` vec axx vec b= vec0\ a n d\ vec adot vec b=0.`

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We have,
` vec axx vec b= vec0`
`=>vec a=0 , or vec b=0 or vec a|\| vec b`
and also given
`vec a * vec b=0.`
`=>vec a=0 , or vec b=0 or vec a bot vec b`
But, `vec a` cannot be both perpendicular as well as parallel to `vec b`
so,`vec a=0 , or vec b=0` .
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