hoopsmax25 said:would it be 1?
hoopsmax25 said:Ok i get that now. So if d(t)=1, which is a constant, then d(t) dotted with d'(t) =0. Since c(t)/||c(t)|| has the same direction as c(t), we can then plug c(t) in for d(t). Does that make sense to do?
The dot product of a vector with the derivative of its unit vector is a scalar value that represents the rate of change of the vector in the direction of its unit vector. It is calculated by multiplying the magnitude of the vector with the cosine of the angle between the vector and its derivative of the unit vector.
In physics, the dot product of a vector with the derivative of its unit vector is useful in calculating the work done by a force on an object. It is also used in calculating the flux of a vector field through a surface and in determining the angle between two vectors.
Yes, the dot product of a vector with the derivative of its unit vector can be negative. This occurs when the angle between the vector and its derivative of the unit vector is greater than 90 degrees. In this case, the cosine of the angle is negative, resulting in a negative dot product.
If the dot product of a vector with the derivative of its unit vector is zero, then the two vectors are said to be orthogonal or perpendicular to each other. This means that the angle between the vector and its derivative of the unit vector is 90 degrees and there is no component of the vector in the direction of its derivative of the unit vector.
No, the dot product of a vector with the derivative of its unit vector is not affected by the length of the vector. This is because the dot product is calculated by multiplying the magnitude of the vector with the cosine of the angle between the vector and its derivative of the unit vector, which does not depend on the length of the vector.