andrewkirk said:What strange terminology! I've not seen anybody use ratios with vectors that way before.
I can only guess that when they say 'P divides AB in the ratio r:s' they mean
$$\frac{\vec{AP}}{r}=\frac{\vec{PB}}{s}$$
Which of your two options does that favour?
Vector divide with negative ratio is a mathematical operation that involves dividing a vector by a negative number. This can result in a change in the direction of the vector, as well as its magnitude.
The main difference between vector divide with negative ratio and regular vector division is the direction of the resulting vector. When dividing a vector by a positive number, the direction remains the same, but when dividing by a negative number, the direction is reversed.
When the numerator of the division is a negative vector, the resulting vector will have a direction that is opposite to the original vector. This is because the negative vector will cancel out the negative ratio, resulting in a positive ratio and a reversed direction.
No, it is not possible to divide a vector by zero. Division by zero is undefined and has no meaning in mathematics. It is important to note that division by a number very close to zero can result in a very large vector, but this is not the same as dividing by exactly zero.
Yes, vector divide with negative ratio can be applied to any type of vector, including 2D and 3D vectors. The resulting vector will have the same number of dimensions as the original vector.