Calculation bug (Please enter information such as specific input values, calculation result, correct result, and reference materials (URL and documents).) Text bug (Please enter information such as wrong and correct texts).Vector addition and subtraction (V - U) The sum of two vectors (V, U) is the vector that results in the sum of the their respective components, such that U V (U x V x, U y V y, U z V z ).
V U - Computes the dot product of two vectors V x U - Computes the cross product of two vectors V x U W - Computes the mixed product of three vectors Vector Angle - Computes the angle between two vectors Vector Area - Computes the area between two vectors Vector Projection - Compute the vector projection of V onto U. Rectangular Coordinate System Calculator How To Use TheRelated Items: For a YouTube video with instructions on how to use the calculator, CLICK HERE. For vectors in Physics, see Light and Matter (Dr. Benjamin Crowell): Vector Notation Calculations with Magnitude and Direction Techniques for adding vectors Vectors and Motion CLICK HERE for a Quaternion Calculator. Dot Product (V U) In mathematics, the dot product, or scalar product (or sometimes inner product in the context of Euclidean space), is an algebraic operation that takes two equal-length sequences of numbers (usually coordinate vectors) and returns a single number. This operation can be defined either algebraically or geometrically. Algebraically, it is the sum of the products of the corresponding entries of the two sequences of numbers. Cartesian (XYZ) Coordinates Two vectors in 3D Vector Cross Product vector addition and subtraction Geometrically, it is the product of the Euclidean magnitudes of the two vectors and the cosine of the angle between them. The name dot product is derived from the centered dot that is often used to designate this operation; the alternative name scalar product emphasizes the scalar (rather than vectorial) nature of the result. This calculator uses the arc-cosine of the dot product to calculate the angle between two vectors after it has converted the vectors into unit vectors. Note: the arc-cosine (cosine inverse) of the dot product of two non-unit vectors does not produce the angle between them. Cross Product (V x U) In mathematics, the cross product or vector product is a binary operation on two vectors in three-dimensional space and is denoted by the symbol. The cross product a b of the vectors a and b is a vector that is perpendicular to both and therefore normal to the plane containing them. It has many applications in mathematics, physics, and engineering. If the vectors have the same direction or one has zero length, then their cross product is zero. More generally, the magnitude of the product equals the area of a parallelogram with the vectors for sides; in particular, for perpendicular vectors, this is a rectangle and the magnitude of the product is the product of their lengths. The cross product is anticommutative (i.e. The space and product form an algebra over a field, which is neither commutative nor associative, but is a Lie algebra with the cross product being the Lie bracket. Like the dot product, it depends on the metric of Euclidean space, but unlike the dot product, it also depends on a choice of orientation or handedness. The product can be generalized in various ways; it can be made independent of orientation by changing the result to pseudovector, or in arbitrary dimensions the exterior product of vectors can be used with a bivector or two-form result. ![]() But if the product is limited to non-trivial binary products with vector results, it exists only in three and seven dimensions. Right Hand Convention: Note that cross product depicted in the diagram has the order of U X V, where U is first. Consider placing ones right hand along the first vector in the operation (U in the diagram). If one then sweeps the hand counter clockwise (normal right hand motion) towards the second vector (V in the diagram), the resulting normal vector (U X V) will be in the direction of ones extended thumb, hence the Right Hand Convention.
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