The right hand rule cross product is a common short word in mathematics and physics for remembering vector notation conventions in three dimensions. British physicist John Ambrose Fleming invented it in the late 1800s for use in electromagnetism.
There are two distinct solutions when selecting three vectors that must be at right angles to each other, so when presenting this concept in mathematics, the uncertainty of which solution is meant must be avoided.
When an order operation is performed on two vectors, x̄ and y̅, a right hand rule cross product, or vector product, is generated. The cross product of vectors x̄ and y̅ is normal to the plane that contains it and perpendicular to both a and b. The right hand rule cross product should be used to decide the direction of the cross product vector since there are two possible paths for a cross product.
The cross product of vectors x̄ and y̅, for example, can be expressed by the equation:
x̄ x y̅ = z̅
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What is Right Hand Thumb Rule Cross Product ?
Align the fingers and thumb at right angles to apply the right hand rule cross product. Then, with your index and middle fingers, point in the direction of vector x̄ and vector y̅, respectively.
What Is Vector ?
In English, the term vector may have several meanings, but in math and physics, a vector corresponds to something very unique. A vector is a mathematical representation of a physical quantity with both a magnitude and a direction, as indicated by arrows, in these fields. It can also be decomposed into components that indicate how much of the vector is present in each direction.
As you can see, a vector can have three-dimensional components: the x, y, and z components of the vector and are represented by x̅, y̅, and z̅. So, what kinds of quantities do vectors represent? Although there are numerous options, the most straightforward is the most likely location. A position vector is a vector that indicates the location of an object of some origin.
This can be shown in the following diagram:
Vectors can be multiplied in two ways, both of which result in the cross product. A cross product indicates which portion of one vector is perpendicular to the other.
The cross product of vectors a̅ and b̅ produces a new vector that is perpendicular to both a̅ and b̅. If you know the magnitudes of vectors a̅ and b̅, multiplying the magnitudes of a, b, and the sine of the angle between them will give you the magnitude of the cross product.
a̅ x b̅ = |a| |b|sinθ
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This equation will give you the cross product vector’s magnitude, but wait! Always keep in mind that vectors have a magnitude and a direction. How can we figure out which way to go? For that, we need the right hand rule cross product.
At the end of The right hand rule can be used to calculate the position of the cross product: the left hand indicates the direction of the gradient vector A, while the pointer finger points in the direction of the current field vector B. The finger is pointing in the direction of F, which is the cross item.
Read More : Cross Product Of Perpendicular Verctors