Mathematics - Vector Question with Solution | TestHub

$a.b.=a\cdot c\Rightarrow a\cdot (b-c)=0$ $\Rightarrow \mathrm{a}=0\mathrm{or}\mathrm{b}-\mathrm{c}=0$ or $\mathrm{a}\perp (\mathrm{b}-\mathrm{c})$ $\Rightarrow \mathrm{a}=0$ or $\mathrm{b}=\mathrm{c}$ or $\mathrm{a}\perp (\mathrm{b}-\mathrm{c})$ Also a $xb=axc\Rightarrow a\times (b-c)=0$ $\Rightarrow \mathrm{a}=0$ or $\mathrm{b}-\mathrm{c}=0$ or a $\Vert (\mathrm{b}-\mathrm{c})$ $\Rightarrow a=0$ or $b=c$ or $a\Vert (b-c)$ Observing to ( 1 ) and ( 2 ) we find that $\mathrm{a}=0$ or $\mathrm{b}=\mathrm{c}$