This post categorized under Vector and posted on April 3rd, 2019.

Cross Product. A vector has magnitude (how long it is) and direction Two vectors can be multiplied using the Cross Product (also see Dot Product) The Cross Product a b of two vectors is another vector that is at right angles to bothThe geometric definition of the cross product is good for understanding the properties of the cross product. However the geometric definition isnt so useful for computing the cross product of vectors. For computations we will want a formula in terms of the components of vectors. We start by using the geometric definition to compute the cross product of the standard unit vectors.Cross-Product Magnitude. The direction of the cross-product vector is then taken to be orthogonal to both and according to the right-hand rule.

Vector formulas dot product cross product scalar triple product vector addition scalar multiplication linearly dependent and independent vectors unit vector magnitude. Vector Formulas Moreover this proof gives an appealing geometric interpretation of the vector cross-product as having magnitude given by the product of times the norm of the difference between and the orthogonal projection of onto () or vice versa ().The vector product of two vectors a and b is given by a vector whose magnitude is given by absin (where0180) which stands for the angle between the two vectors. Note that the direction of the resultant vector is denoted by a unit vector n whose direction is perpendicular to both the vectors a and b in a way that a b and n are oriented in right-handed system.

This formula shows that the magnitude of the cross product is largest when vca and vcb are perpendicular. On the other hand if vca and vcb are parallel or if either vector is the zero vector then the cross product is the zero vector.The cross product a b (vertical in purple) changes as the angle between the vectors a (blue) and b (red) changes. The cross product is always orthogonal to both vectors and has magnitude zero when the vectors are parallel and maximum magnitude ab when they are orthogonal.

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