Work in formula in dot smoothly

Aug 6th, 2022
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How to Work in formula in dot

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so dot product is a mathematical tool for dealing with vectors so if I have a vector a and I have some other vector B and I want to calculate the dot product how do I visualize it first off I put the vectors together and then I figure out the angle between them the dot product is this a dot B is defined as magnitude of a times magnitude of B times cosine of the angle between them it's the projection of one vector onto the other this is a scalar so this is known as the scalar product so if you hear those words it's the same thing as dot product dot product or scalar product because there's no vectors on the right-hand side here okay you took two vectors and got rid of the vector signs by writing it as this scalar product so back to the question that we just had if we have C dot C what do we get we get magnitude of C times magnitude of C times cosine of the angle between them what's the angle between C and C 0 and cosine of 0 is 1 and so we do just get C squared so dot products we're go...

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So, for example, work is force multiplied by displacement. Its two vectors multiplied together. But more specifically its the force acting in the direction youre moving, multiplied by the displacement. This is why work is a dot product.
Show that work done is equal to the dot product of force and displacement. Solution : Work : Work is said to be done, when force applied on a body displaces it through a distance in the direction of applied force. The work done is the product of the displacement and component of force in the direction of displacement.
The difference between the dot product and the cross product of two vectors is that the result of the dot product is a scalar quantity, whereas the result of the cross product is a vector quantity. The result is a scalar quantity, so it has only magnitude but no direction.
Show that work done is equal to the dot product of force and displacement. Solution : Work : Work is said to be done, when force applied on a body displaces it through a distance in the direction of applied force. The work done is the product of the displacement and component of force in the direction of displacement.
Work done is the product of force and and it acts in the direction of the applied force .
My question : Why is work a scalar quantity? Their answer : Because it is the dot product of Force and Displacement. So it is a scalar quantity.
The dot product is equal to the sum of the product of the horizontal components and the product of the vertical components. This same equation could be solved for theta if the angle between the vectors needed to be determined.
The dot product is a fundamental way we can combine two vectors. Intuitively, it tells us something about how much two vectors point in the same direction.
The vector dot product multiplies the components of two vectors that are parallel to each other. By multiplying the x components together and adding that to the multiplied y components, we can get the Work, which is a scalar value.
2:29 4:58 Work and the Dot Product - YouTube YouTube Start of suggested clip End of suggested clip So this dot product here for my work its exactly equivalent numerically to taking the magnitudesMoreSo this dot product here for my work its exactly equivalent numerically to taking the magnitudes and multiplying them but then I also have to multiply the angle in there.

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