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engstudent363
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Anyone familiar with dot products of two vectors? What does the dot product show, in other words what is the point of doing a dot product?
By using [t e x]symbol notation here[/t e x] or [i t e x]symbol notation here[/i t e x].engstudent363 said:thank you sir. i think i understand it now. By the way, how did you make those cool symbols like for theta or the dot in between v1 and v2
Well, I certainly wouldn't put it that way. It is common to think of Force as a vector but "distance" is just a number. I would say Work = Force•displacement.flebbyman said:The dot product has another useful use:
Work = Force•distance
HallsofIvy said:Well, I certainly wouldn't put it that way. It is common to think of Force as a vector but "distance" is just a number. I would say Work = Force•displacement.
A dot product, also known as an inner product, is a mathematical operation that takes two vectors and produces a scalar value. In multivariable calculus, the dot product is used to find the angle between two vectors and to project one vector onto another.
The dot product is calculated by taking the product of the corresponding components of two vectors and then summing up those products. For example, if vector A is (a1, a2, a3) and vector B is (b1, b2, b3), then the dot product A · B = (a1 * b1) + (a2 * b2) + (a3 * b3).
The dot product can be interpreted geometrically as the product of the magnitudes of two vectors and the cosine of the angle between them. This means that the dot product will be larger when the vectors are parallel and smaller when they are perpendicular.
The dot product is closely related to orthogonality, or perpendicularity, of two vectors. If the dot product is equal to 0, then the vectors are orthogonal to each other. This means that they are at a 90 degree angle to each other and have no component in the same direction.
The dot product has many applications in multivariable calculus, including finding the work done by a force moving an object, determining the rate of change of a function in a given direction, and finding the equation of a plane using a normal vector. It is also used in optimization problems and in calculating surface area and volume of three-dimensional objects.