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In mathematics and physics, the right-hand rule is a convention and a mnemonic, utilized to define the orientation of axes in three-dimensional space and to determine the direction of the cross product of two vectors, as well as to establish the direction of the force on a current-carrying conductor in a magnetic field.
(b) The right-hand rule is used to determine the placement of the coordinate axes in the standard Cartesian plane. In two dimensions, we describe a point in the plane with the coordinates \((x,y)\). Each coordinate describes how the point aligns with the corresponding axis.
Using the right-hand rule to find the direction of the cross product of two vectors in the plane of the page.
The Right-Hand Rule is an easy way to find the direction of a cross product interaction before doing the math. For any equation involving a cross product, the right hand rule is a valuable tool for finding the direction.
Its length is given by \(‖\vecs u×\vecs v‖=‖\vecs u‖⋅‖\vecs v‖⋅\sin θ,\) where \(θ\) is the angle between \(\vecs u\) and \(\vecs v\). Its direction is given by the right-hand rule. The algebraic formula for calculating the cross product of two vectors, \(\vecs u= u_1,u_2,u_3 \) and \(\vecs v= v_1,v_2,v_3 \), is
The right-hand rule states that the orientation of the vectors' cross product is determined by placing u and v tail-to-tail, flattening the right hand, extending it in the direction of u, and then curling the fingers in the direction that the angle v makes with u.
The direction of the cross product vector A x B is given by the right-hand rule for the cross product of two vectors. To apply this right-hand rule, extend the fingers of your right hand so that they are pointing directly away from your right elbow.
The cross product a × b is defined as a vector c that is perpendicular (orthogonal) to both a and b, with a direction given by the right-hand rule [1] and a magnitude equal to the area of the parallelogram that the vectors span.
The right-hand rule is a convention used in physics and mathematics to determine the direction of a vector resulting from a cross product, often applied in the context of rotations and orientations in three-dimensional space.
The right-hand rule is an intuitive way of visualizing vector directions in 3D. It is easy to remember and apply, and it works for any two vectors that are perpendicular to each other. The rule is not only limited to the right hand but can also be applied using the left hand by reversing the direction of the vectors.