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woodie37
- 14
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Can someone explain to me what a dot product and vector product of two vectors are? Be as detailed as possible please! And also why does the right hand rule for vectors work?
A vector cross product is a mathematical operation that takes two vectors as input and produces a third vector that is perpendicular to both of the input vectors. It is denoted by the symbol "×" and is also known as the vector product or cross product.
The vector cross product can be calculated using the formula a × b = ||a|| ||b|| sinθ n, where a and b are the two input vectors, ||a|| and ||b|| are their magnitudes, θ is the angle between them, and n is a unit vector perpendicular to both a and b in the direction determined by the right-hand rule.
The dot and cross product have various applications in physics, such as calculating work, torque, and magnetic fields. The dot product is used to find the component of one vector in the direction of another, while the cross product is used to find the component perpendicular to both vectors.
The vector cross product and dot product are related through the distributive property. This means that the cross product of two vectors is equal to the dot product of one vector with the cross product of the other vector with a unit vector in the direction of the first vector.
Yes, the magnitude of the vector cross product of two vectors is equal to the area of the parallelogram formed by those two vectors. This property is often used in geometric and trigonometric proofs.