If vec{a} cdot vec{a}=0 and vec{a} cdot vec{b | vedclass

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(C) Given that $\vec{a} \cdot \vec{a}=0$ and $\vec{a} \cdot \vec{b}=0$.From the property of the dot product,$\vec{a} \cdot \vec{a} = |\vec{a}|^2$.Sinc

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$\vec{b}$ can be any vector.

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(C) Given that $\vec{a} \cdot \vec{a}=0$ and $\vec{a} \cdot \vec{b}=0$.From the property of the dot product,$\vec{a} \cdot \vec{a} = |\vec{a}|^2$.Since $\vec{a} \cdot \vec{a} = 0$,we have $|\vec{a}|^2 = 0$,which implies $|\vec{a}| = 0$.Therefore,$\vec{a}$ is a zero vector $(\vec{a} = \vec{0})$.Now,consider the second condition $\vec{a} \cdot \vec{b} = 0$. Since $\vec{a} = \vec{0}$,the equation becomes $\vec{0} \cdot \vec{b} = 0$.This equation holds true for any vector $\vec{b}$ in the space.Thus,$\vec{b}$ can be any vector.

If $\vec{a} \cdot \vec{a}=0$ and $\vec{a} \cdot \vec{b}=0,$ then what can be concluded about the vector $\vec{b}$?

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