Question
Define and explain vector product of two vectors with suitable examples.
✓
Answer
i. The vector product of two vectors is a third vector whose magnitude is equal to the product of magnitude of the two vectors and sine of the smaller angle θ between the two vectors.
ii. Vector product is also called cross product of vectors because cross sign is used to represent vector product.
iii. Explanation:
a. The vector product of two vectors$\overrightarrow{ A }$ and $\overrightarrow{ AB}$, is a third vector $\overrightarrow{ R }$ and is written as, $\overrightarrow{ R }$ = $\overrightarrow{ A }$ × $\overrightarrow{ B }$ = AB sin $\theta \hat{ u }_{ r }$ where, $\hat{ u }_{ r }$ is unit vector in direction of $\overrightarrow{ R }$, i.e., perpendicular to plane containing two vectors. It is given by right handed screw rule.
c. Examples of vector product:
1. Force experienced by a charge q moving with velocity $\overrightarrow{ V }$ in uniform magnetic field of induction (strength) $\overrightarrow{ B }$ is given as $\overrightarrow{ F }$ = $q \vec{V}$ × $\overrightarrow{ B}$
2. Moment of a force or torque$\binom{\rightarrow}{\tau}$ is the vector product of the position vector $(\vec{r})$ and the force $(\overrightarrow{ F })$.
i.e., $\vec{\tau}=\overrightarrow{ r } \times \overrightarrow{ F }$
3. The instantaneous velocity $(\vec{v})$ of a rotating particle is equal to the cross product of its angular velocity $(\vec{\omega})$ and its position $(\overrightarrow{ r })$ from axis of rotation.
$\overrightarrow{ v }=\overrightarrow{ r } \times \vec{\omega}$
ii. Vector product is also called cross product of vectors because cross sign is used to represent vector product.
iii. Explanation:
a. The vector product of two vectors$\overrightarrow{ A }$ and $\overrightarrow{ AB}$, is a third vector $\overrightarrow{ R }$ and is written as, $\overrightarrow{ R }$ = $\overrightarrow{ A }$ × $\overrightarrow{ B }$ = AB sin $\theta \hat{ u }_{ r }$ where, $\hat{ u }_{ r }$ is unit vector in direction of $\overrightarrow{ R }$, i.e., perpendicular to plane containing two vectors. It is given by right handed screw rule.
c. Examples of vector product:
1. Force experienced by a charge q moving with velocity $\overrightarrow{ V }$ in uniform magnetic field of induction (strength) $\overrightarrow{ B }$ is given as $\overrightarrow{ F }$ = $q \vec{V}$ × $\overrightarrow{ B}$
2. Moment of a force or torque$\binom{\rightarrow}{\tau}$ is the vector product of the position vector $(\vec{r})$ and the force $(\overrightarrow{ F })$.
i.e., $\vec{\tau}=\overrightarrow{ r } \times \overrightarrow{ F }$
3. The instantaneous velocity $(\vec{v})$ of a rotating particle is equal to the cross product of its angular velocity $(\vec{\omega})$ and its position $(\overrightarrow{ r })$ from axis of rotation.
$\overrightarrow{ v }=\overrightarrow{ r } \times \vec{\omega}$
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