Question

Given that $\vec{a}.\vec{b}=0$ and $\vec{a}\times\vec{b}=0$.What can you conclude about the vectors $\vec{a}$ and $\vec{b}$ ?

Answer 1

$\vec{a}.\vec{b}=0$
Then,
(i)Either$|\vec{a}|=0\space or \space |\vec{b}|=0\space or\space \vec{a}\perp\vec{b}$ (in case $\vec{a}$ and $\vec{b}$ are non-zero)
$\vec{a}\times\vec{b}=0$
(ii)Either$|\vec{a}|=0$ or $|\vec{b}|=0$,or $\vec{a}\parallel\vec{b}$ (in case $\vec{a}$ and $\vec{b}$ are non-zero)
But, $\vec{a}$ and $\vec{b}$ cannot be perpendicular and parallel simultaneously.
Hence$,|\vec{a}|=0$ or$|\vec{b}|=0$.