the method i have tried is really useless?radou said:Try to think of an example where it's not true.
assume b is not equal to cradou said:It's not useless, it just doesn't tell you anything.
You can solve this by finding a counterexample.
zero =[radou said:let a = (1, 0, 0), b = (1, 0, 1), c = (1, 2, 1).
What does a.(b - c) equal?
a.(b - c) = 0, when b doesn't equal cradou said:It doesn't matter what you use.
If you're not talking about a specific set of vectors and a specific dot product, and if you assume that, for any non-zero a, and any b, c, the implication a.(b - c) = 0 ==> b = c holds (which is equivalent to a.b = a.c ==> b = c) then it doesn't matter which vector space and dot product you chose to construct your counterexample.
So, we found an example where a.(b - c) = 0, when b doesn't equal c.
Vector equivalence refers to the condition where two vectors have the same magnitude and direction.
Vector equivalence can be proven by showing that the dot product (a‧b) and (a‧c) of the two vectors are equal. This means that the angles between the two vectors are the same, and therefore they have the same direction.
Vector equivalence is important in mathematics and physics as it allows us to simplify and solve problems involving vectors. It also helps us understand the relationship between different vectors.
Yes, vector equivalence can be applied to all types of vectors, including 2D and 3D vectors, as long as they have the same magnitude and direction.
Vector equivalence is closely related to vector addition and subtraction. If two vectors are equivalent, then they can be added or subtracted to create a new vector with the same magnitude and direction.