Statement I: If $\vec{a}$ and $\vec{b}$ are two non-zero vectors. If $\vec{c}=\vec{a}+\vec{b}$, then

Question

Statement I: If $\vec{a}$ and $\vec{b}$ are two non-zero vectors. If $\vec{c}=\vec{a}+\vec{b}$, then $\vec{c} \cdot \vec{a}=0$ and $\vec{c} \cdot \vec{b}=0$. \  Statement II : If $\vec{c}=\vec{a}+\vec{b}, \vec{c}$ is perpendicular to $\vec{a}$ and $\vec{b}$.

Professor PC Thomas Classes · Answer

(a) : If $\vec{c}=\vec{a} 	imes \vec{b}$ The angle between $\vec{c}$ and $\vec{a}$ and $\vec{c}$ and $\vec{b}$ are $\frac{\pi}{2}$. $$ 	herefore \quad \vec{c} \cdot \vec{a}=|\vec{c}||\vec{a}| \cos 90^{\circ}=0 $$ and $\vec{c} \cdot \vec{b}=|\vec{c}||\vec{b}| \cos 90^{\circ}=0$