Question

Two vectors are perpendicular, if

• A. $\vec{A}\cdot \vec{B}\cdot =1$
• B. $\vec{A}\cdot \vec{B}\cdot =0$
• C. $\vec{A}\cdot \vec{B}=0$
• D. $\vec{A}\cdot \vec{B}=AB$

Answer 1

Answer: (C)

Condition of orthogonality is that scalar product of two vectors must be zero. The scalar product (or dot product) of two vectors is defined as the product of the magnitudes of two vectors with cosine of angle between them.
Thus, if there are two vectors $\vec{A}$ and $\vec{B}$ having angle $\theta$ between them, then their scalar product $\vec{A}\cdot \vec{B}$ is written as $\vec{A}\cdot \vec{B}=AB\cos \theta$ Scalar product of two vectors will be minimum when $|\cos \theta |=\min =0$, ie. $\theta =90^{\circ }$
$\therefore (\vec{A}.\vec{B}{)}_{\min }=0$ ie, if the scalar product of two non-zero vectors vanishes, the vectors are orthogonal.