Consider the following statements :Statement | vedclass

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(A) Statement $(I)$ : The dot product of two vectors $\vec{a}$ and $\vec{b}$ is defined as $\vec{a} \cdot \vec{b} = |\vec{a}| |\vec{b}| \cos 	heta$.

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Statement $(I)$ is false but Statement $(II)$ is false

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(A) Statement $(I)$ : The dot product of two vectors $\vec{a}$ and $\vec{b}$ is defined as $\vec{a} \cdot \vec{b} = |\vec{a}| |\vec{b}| \cos 	heta$. If $|\vec{a}|=0$ or $|\vec{b}|=0$,then $\vec{a} \cdot \vec{b} = 0 	imes |\vec{b}| \cos 	heta = 0$ or $\vec{a} \cdot \vec{b} = |\vec{a}| 	imes 0 	imes \cos 	heta = 0$. Thus,Statement $(I)$ is true.Statement $(II)$ : The cross product of two vectors is defined as $\vec{a} 	imes \vec{b} = |\vec{a}| |\vec{b}| \sin 	heta \hat{n}$. If $\vec{a} 	imes \vec{b} = \vec{0}$,then $\sin 	heta = 0$,which implies $	heta = 0$ or $	heta = \pi$. This means the vectors are parallel or collinear,not perpendicular. Thus,Statement $(II)$ is false.

Consider the following statements :
Statement $(I)$ : If either $|\vec{a}|=0$ or $|\vec{b}|=0$,then $\vec{a} \cdot \vec{b}=0$.
Statement $(II)$ : If $\vec{a} \times \vec{b}=\vec{0}$,then $\vec{a}$ is perpendicular to $\vec{b}$.
Which of the following is correct?

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Consider the following statements :Statement $(I)$ : If either $|\vec{a}|=0$ or $|\vec{b}|=0$,then $\vec{a} \cdot \vec{b}=0$.Statement $(II)$ : If $\vec{a} \times \vec{b}=\vec{0}$,then $\vec{a}$ is perpendicular to $\vec{b}$.Which of the following is correct?