Question

How do you use the right-hand rule for cross-product?

Answer 1

Mention the right-hand rule of Fleming.
According to Fleming's Right-Hand Rule, if we arrange our right hand's thumb, forefinger, and middle finger perpendicular to one another, the thumb will point in the direction of the magnetic force, the forefinger will point in the direction of the magnetic field, and the middle finger will point in the direction of the current.

The purpose of Fleming’s right-hand rule is to find the direction of induced current when a conductor moves in a magnetic field.

Fleming’s right-hand rule is used for electric generators.

1. The right-hand thumb rule is used to determine the direction of the vector obtained by the cross-product of two vectors.
2. Let us find the cross product of a and b, $\overrightarrow{a}\times \overrightarrow{b}=\overrightarrow{c}$, as a vector $c$ is perpendicular (orthogonal) to both the vectors,
3. The magnitude of $\overrightarrow{a}\times \overrightarrow{b}$ is equal to the area of the parallelogram formed by the vectors spanned by vectors a and b and the resultant vectors' direction obtained by applying the right-hand rule.
4. The cross product gives the way two vectors differ in their direction.

Use the following steps to use the right-hand rule:
First, hold up your right hand and make sure it's not your left,

1. Point your index finger in the direction of the first vector, let $\overrightarrow{a}$.
2. Point your middle finger in the direction of the second vector, let $\overrightarrow{b}$.
3. Your thumb point gives the direction of the cross product.
4. Note that: $\overrightarrow{a}\times \overrightarrow{b}\ne \overrightarrow{b}\times \overrightarrow{a}$ .