CORK SCREW RULE: The vector C  is normal to the plane of A and B   are points in the direction in which a right handed screw would advance when rotated about an axis perpen- dicular to the plane of the two vectors in the direction from A to B   through the smaller angle  between them or, alternatively, we might state the rule as: If the fingers of the right hand be curled in the direction in which vector A  must be turned through the smaller included angle  to coincide with the direction of vector B  , the thumb points in the direction of C  as shown in figure. Either of these rules is referred to as the right handed screw rule. Thus, if nˆ be the unit vector in the direction of C  , we have C A B ABsin n    ˆ    where 0     .

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The Right-Hand Rule, also known as the Corkscrew Rule, is a fundamental concept in vector mathematics. It determines the direction of the cross product of two vectors A and B. The resulting vector C is always perpendicular to the plane containing both A and B. The corkscrew rule states that vector C is normal to the plane of A and B, pointing in the direction a right-handed screw would advance when rotated about an axis perpendicular to the plane from A to B through the smaller angle between them. Alternatively, we can use the right-hand finger rule. If the fingers of the right hand curl in the direction from vector A to vector B through the smaller included angle, the thumb points in the direction of the cross product vector C. The mathematical formula for the cross product is C equals A cross B. The magnitude of C equals the magnitude of A times the magnitude of B times sine of theta, where theta is the angle between the vectors and ranges from 0 to 180 degrees. The direction is given by the unit vector n-hat as determined by the right-hand rule. The corkscrew rule states that vector C is normal to the plane of A and B, pointing in the direction a right-handed screw would advance when rotated about an axis perpendicular to the plane from A to B through the smaller angle between them. Alternatively, we can use the right-hand finger rule. If the fingers of the right hand curl in the direction from vector A to vector B through the smaller included angle, the thumb points in the direction of the cross product vector C. The mathematical formula for the cross product is C equals A cross B. The magnitude of C equals the magnitude of A times the magnitude of B times sine of theta, where theta is the angle between the vectors and ranges from 0 to 180 degrees. The direction is given by the unit vector n-hat as determined by the right-hand rule. The Cork Screw Rule, also known as the Right-Hand Rule, is a fundamental concept in vector mathematics. It determines the direction of the cross product C equals A cross B. The resulting vector C is always normal, or perpendicular, to the plane containing vectors A and B. The screw rule works like this: Imagine a right-handed screw placed perpendicular to the plane containing vectors A and B. When you rotate the screw from vector A toward vector B through the smaller angle between them, the direction the screw advances gives you the direction of the cross product vector C. Alternatively, you can use the finger method. Point your fingers along vector A, then curl them toward vector B through the smaller angle between the vectors. Your thumb will naturally point in the direction of the cross product vector C. This gives the same result as the screw rule. The mathematical formula for the cross product combines magnitude and direction. The magnitude of C equals the product of the magnitudes of A and B times the sine of the angle between them. The complete vector formula shows that C equals A cross B, which equals this magnitude times the unit vector n-hat in the direction determined by the right-hand rule. The Right-Hand Rule has numerous applications in physics, engineering, computer graphics, and robotics. It's essential for understanding magnetic fields, torque calculations, normal vectors, and rotation directions. Remember the key points: the cross product vector C is always perpendicular to both A and B, its direction follows the right-hand rule, and its magnitude equals the product of the magnitudes times sine of the angle between them.