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It comes from the Law of Cosines.

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For any two vectors A and B, the projection of A onto B, that is, the component of A along B, is ab.cos(x) where x is the angle between the two vectors. By symmetry, this is also the projectoin of B onto A.

Q: Why you are using cosine function in dot product of two vectors?

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A x B = |A| |B| sin[theta]

Work is defined as the dot product of force times distance, or W = F * d = Fd cos (theta) where theta is the angle in between the force and distance vectors (if you are doing two dimensions). In three dimensions, use the standard definition for the dot product (using the component form of the vectors).

The "vector triangle" illustrates the "dot product" of two vectors, represented as sides of a triangle and the enclosed angle. This can be calculated using the law of cosines. (see link)

They are different trigonometric functions!

1) Separate the vectors into components (if they are not already expressed as components). 2) Add each of the components separately. 3) If required, convert the vectors back to some other form. For twodimensional vectors, that would polar form.

Related questions

A vector rotation in math is done on a coordinate plane.2D vectors can be rotated using the cross and dot product.3D vectors are rotated using matrix based quaternion math.

A x B = |A| |B| sin[theta]

Sine allows us to find out what a third side or an angle is using the equation sin(x) = opposite over hypotenuse (x being the angle). Cosine has the same function but instead uses the equation cosine(x)= opposite over adjacent

"addition and subtraction"Resultant velocity refers to the sum of all vectors in an equation. The two math functions that are used to calculate the resultant velocity are addition and subtraction.

Work is defined as the dot product of force times distance, or W = F * d = Fd cos (theta) where theta is the angle in between the force and distance vectors (if you are doing two dimensions). In three dimensions, use the standard definition for the dot product (using the component form of the vectors).

When performing the cross product of two vectors (vector A and vector B), one of the properites of the resultant vector C is that it is perpendicular to both vectors A & B. In two dimensional space, this is not possible, because the resultant vector will be perpendicular to the plane that A & B reside in. Using the (i,j,k) unit vector notation, you could add a 0*k to each vector when doing the cross product, and the resultant vector will have zeros for the i & jcomponents, and only have k components.Two vectors define a plane, and their cross product is always a vector along the normal to that plane, so the three vectors cannot lie in a 2D space which is a plane.

The "vector triangle" illustrates the "dot product" of two vectors, represented as sides of a triangle and the enclosed angle. This can be calculated using the law of cosines. (see link)

manipulate the function algebraically, so that the result is easier to differentiate

They are different trigonometric functions!

A scalar is a real quantity like distance and a vector is a vector quantity like displacement.Displacement is the product of a distance and a direction,Displacement =DistancexDirection.

1) Separate the vectors into components (if they are not already expressed as components). 2) Add each of the components separately. 3) If required, convert the vectors back to some other form. For twodimensional vectors, that would polar form.

If you know the angle's sine, cosine, or tangent, enter it into the calculator and press <inverse> sine, cosine, or tangent. On MS Calc, in Scientific Mode, using Degrees, enter 0.5, then check Inv and the press sin. You should get 30 degrees. The other functions work similarly.