Right-Hand Rule Cross Product

The right-hand thumb rule for the cross-product of two vectors aids in determining the resultant vector’s direction. The orientation of a vector is the angle it makes with the x-axis, which is its direction. A vector is created by drawing a line with an arrow at one end and a fixed point at the other. The vector’s direction is determined by the direction in which the arrowhead is pointed. Velocity, for example, is a vector. It indicates the magnitude of the object’s movement as well as the direction in which the object is moving.

The right hand rule can be used to determine the direction of the cross product as follows:

The index finger is pointing in the velocity vector v direction. The magnetic field vector B is represented by the middle finger. The thumb is pointing towards the cross product F.

Cross Product

The cross product a b is defined as a vector c that is perpendicular (orthogonal) to both a and b, with a magnitude equal to the area of the parallelogram that the vectors span and a direction given by the right-hand rule. The cross product determines how far two vectors differ in their directions.

Right-hand Rule – Cross Product

The right-hand thumb rule for the cross-product of two vectors aids in determining the resultant vector’s direction. Our thumb will point in the direction of the cross product of the two vectors if we point our right hand in the direction of the first arrow and curl our fingers in the direction of the second. The cross product formula for determining the direction of the resultant vector is given by the right-hand thumb rule.

The right-hand rule can be used to determine the direction of the vector that results from the cross product of two vectors. To determine the direction of the cross product of two vectors, we use the following procedure:

• Align your index finger to the first vector’s direction (A^→)  

• Align the middle finger in the second vector B  direction(B^→)

• Now the thumb points in the direction of the cross product of two vectors

We must first raise your right hand to see the right hand rule. If it’s our left, it won’t work. Hold index, middle, and thumb perpendicular to each other, as if you were using an x, y, and z coordinate system. Rotate our hand so that your index finger points in the vector a direction and our middle finger points in the vector b direction. The direction of the cross product a x b will be indicated by our thumb.

When calculating a cross product, be cautious about mixing up the vectors. The order matters, though: a x b does not equal b x a.

Which direction of the resultant vector?

The cross product can point in any direction while remaining at right angles to the other two vectors, so we have:

Point your index finger along vector a and your middle finger along vector b with your right hand: the cross product goes in the direction of your thumb.

The resultant’s direction can be determined by measuring the angle the resultant makes with the north-south or east-west vectors. The angle theta (Θ) is marked inside the vector addition triangle in the diagram to the right. Theta is the angle formed by the resultant with respect to west.

The direction of the resultant vector, for the cross product of two non-parallel vectors, is represented by the right hand rule.

Conclusion

In this article we conclude that Cross products are a type of “difference” measure that compares two vectors (in opposition to the dot product which is a measure of the “sameness” between two vectors). The magnitude of a cross product is proportional to the perpendicularity of the two vectors. For the cross product of two non-parallel vectors, the right hand rule is used to represent the direction of the resultant vector. The direction of the resultant vector is denoted by the thumb if we point our index finger along vector A and our middle finger along vector B.