Final answer:
The magnitude of the resultant vector of two vectors with equal magnitude and opposite direction is zero. Two vectors that are orthogonal to each other are at a 90-degree angle. Vector multiplication is anticommutative, meaning the direction of the product changes when the order of the vectors is reversed.
Step-by-step explanation:
In the context of vector mathematics, when two vectors have equal magnitude but opposite directions, they are considered to be antiparallel. The magnitude of their resultant vector is zero because they cancel each other out when they are added together.
This is due to the principle that adding a vector to its negative results in a zero vector. For example, if vector U has a magnitude of 5 units in a certain direction, its negative, -U, would have the same magnitude but in the opposite direction. The resultant vector of U + (-U) = 0.
Additionally, two vectors that are orthogonal to each other are at a 90-degree angle, not 270 degrees. If vector A is orthogonal to vector B, it means they will not affect each other's magnitude when they are added together, because they are perpendicular.
The concept of magnitude and direction is central in understanding vectors, especially when multiplying vectors, as vector multiplication is not commutative but anticommutative. This means that a vector product, such as A x B, is perpendicular to the plane containing A and B and the result changes sign when the order of multiplication is reversed.