Which of the following physical quantities can be expressed as the vector product of two vectors?

Option (4)

CONCEPT:

• Vector Product (cross product): Its magnitude is equal to the products of the magnitude of two vectors and sine of the angle between them and whose direction is perpendicular to the plane of the two vectors 

Mathematically it is written as: 

\(\vec {A} \) × \(\vec {B}\) = ABsinθ 

Where θ is the angle between a vector \(\vec {A} \) and \(\vec {B}\) 

• Torque, Angular momentum, and Instantaneous velocity all can be expressed as the vector products of two vectors.

EXPLANATION:

• Torque (τ): The torque acting on a particle is equal to the vector products of its position vector \( \vec r \)and force vector \(\vec F\)

τ = \({\vec r \times }{\vec F}\)

• Angular momentum (L): It is equal to the cross product of its position vector \( \vec r \) and the linear momentum \(\vec p\).

\(\vec L\) = \( \vec r \)× \(\vec p\)

• Linear Velocity (v): It is equal to the cross product of its angular velocity ω and the position vector \( \vec r \).

\(\vec v\) = \(\vec \omega \) × \( \vec r \)

• These physical quantities can be expressed as the vector products of two vectors. 
• Hence all of the above options are correct.