what ic the difference between cross product and dot product why can't we calculate work using cross product

Answer 1

The vector cross product gives you another vector which is normal to both of the original vectors, with a magnitude equal to the area subtended by the two. The dot product gives you a scalar. Work, being energy, is a scalar, not a vector. That's why you cannot calculate work using a cross product.

Answer 2

The "dot" or "inner" product of two vectors is the sum of the vector component products. This can be represented as a matrix multiplication.

row vector (1x3) *column vector (3x1) = scalar (1x1).


The "cross" or "outter" product is related to the vector product when you reverse the order of the matrix multiplication. Because the cross product result must map back to a 3-D space (vector), the unit vector cross products are defined in the following way:
i x i = 0, j x j = 0, k x k = 0.
i x j = k, j x k = i, k x i = j.
i x k = -j, k xj = -i, j x i = -k.

column vector (3x1)*row vector (1x3) = matrix (3x3).

To get the cross product vector, the 3x3 matrix entries keeping track of the crossed vector component terms are summed. This results in a vector that is orthogonal to both the output vectors, because the cross product of the unit vectors are defined to be orthogonal. There is a short cut for finding the cross product, and this involves calculating a determinate of a 3x3 matrix with rows of the component vector, first vector and second vector. The short-cut is all most textbooks (and instructors) will show you, and it doesn't really help with understanding what the cross product means.

Now, back to your question. The dot product is used for finding the magnitude of the part of a vector in a given direction. One form of work is done when a force is applied over a given distance. The only force that actually does work is the one that results in movement. So to calculate the work, you are only interested in the part of the force vector that is in the same direction as the displacement.

To calculate the work done by a force that causes a rotation needs to use the cross product. The work in this case is the dot product of a torque vector, which is the cross product of the force and radius vectors, and the rotation vector, which points along the axis of rotation, and the magnitude is how far the object rotates.

You can't calculate work by using a cross product, because the cross product produces a vector that is orthogonal to the two input vectors. Work is a scalar in that it represents the magnitude of a force in a given direction times the movement in that direction.

Answer 3

i'm able to't rather undergo in concepts. yet I do remember a version of Maxwell's equations written in vector style, and that i imagine the stress on a cost transferring in a magnetic field is a vector made from speed and field ability

Answer 4

dot product refers scalar. i.e. result of dot product is scalar.in dot product of vectors only co linear component of vectors does matter.normal component has no role. as in work force multiplied by displacement (in direction of force) OR displacement multiplied by force( in direction of displacement). in vector product normal component is taken into account . thus it is the parallel or perpendicular component of vector which differenciate a result of scalar or vector.