Ammar w said:
Vectors are mathematical objects that have both magnitude (size) and direction. They can be represented by arrows, with the length of the arrow representing the magnitude and the direction of the arrow representing the direction. Unlike regular numbers, which only have magnitude, vectors also have direction.
To add two vectors, you must add their corresponding components. For example, if vector A has components (x1, y1) and vector B has components (x2, y2), then the sum of the two vectors would be (x1 + x2, y1 + y2). This is also known as the "head-to-tail" method, where you place the tail of one vector at the head of the other and draw a line from the tail of the first vector to the head of the second vector, representing the sum of the two vectors.
Yes, vectors can be subtracted from each other. This is done by subtracting the corresponding components, similar to vector addition. For example, if vector A has components (x1, y1) and vector B has components (x2, y2), then the difference of the two vectors would be (x1 - x2, y1 - y2).
The result of adding a vector to its negative vector is always a vector with zero magnitude (also known as the zero vector). This is because the negative vector has the same magnitude as the original vector, but in the opposite direction. When added together, the two vectors cancel each other out.
No, vectors with different dimensions cannot be added or subtracted. In order to add or subtract vectors, they must have the same number of components. For example, a 2-dimensional vector (x, y) cannot be added to a 3-dimensional vector (x, y, z) as they have different dimensions and therefore cannot be combined.