Physics - Vectors Question with Solution | TestHub

If $\vec{A}\cdot \vec{B}=0$, the vectors are perpendicular (or one is zero). If $\vec{A}\times \vec{B}=\vec{0}$, the vectors are parallel (or one is zero). Both conditions imply that at least one of the vectors must be a zero vector. If $\vec{A}\cdot \vec{B}=|\vec{A}||\vec{B}|$, then $AB\cos \theta =AB$, which means $\cos \theta =1$, so $\theta =0^{\circ }$. Thus, $\vec{A}$ and $\vec{B}$ are parallel. If $|\vec{A}\times \vec{B}|=|\vec{A}||\vec{B}|$, then $AB\sin \theta =AB$, which means $\sin \theta =1$, so $\theta =90^{\circ }$. Thus, $\vec{A}$ and $\vec{B}$ are perpendicular.

If $\vec{A}+\vec{B}+\vec{C}=\vec{0}$ and $|\vec{A}|=|\vec{B}|=|\vec{C}|$, the vectors form an equilateral triangle when placed head-to-tail. The angle between any two vectors (when placed tail-to-tail) is $120^{\circ }$.