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The cross product results in a vector quantity that follows a right hand set of vectors; commuting the first two vectors results in a vector that is the negative of the uncommuted result, ie A x B = - B x A
The dot product results in a scalar quantity; its calculation involves scalar (ie normal) multiplication and is unaffected by commutation of the vectors, ie A . B = B . A
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What are the applications of cross product and dot product in physics?
cross: torque dot: work
in what components dot and cross product resolve?
A dot product is a scalar product so it is a single number with only one component. A cross product or vector product is a vector which has three components like the original vectors.
Is work is the vector product of force and distance?
Yes and no. It's the dot product, but not the cross product.
Why you use cosine theta with cross product?
Normally you use sine theta with the cross product and cos theta with the vector product, so that the cross product of parallel vectors is zero while the dot product of vectors at right angles is zero.
What are the applications of cross product and dot product?
Cross product tests for parallelism and Dot product tests for perpendicularity. Cross and Dot products are used in applications involving angles between vectors. For example given two vectors A and B; The parallel product is AxB= |AB|sin(AB). If AXB=|AB|sin(AB)=0 then Angle (AB) is an even multiple of 90 degrees. This is considered a parallel condition. Cross product tests for parallelism. The perpendicular product is A.B= -|AB|cos(AB) If A.B = -|AB|cos(AB) = 0 then Angle (AB) is an odd multiple of 90 degrees. This is considered a perpendicular condition. Dot product tests for perpendicular.
