A vector is a mathematical quantity that has both magnitude (size) and direction. When referring to a vector with magnitude A and direction B, it means that the vector has a specific length (A) and is pointing in a specific direction (B).
The magnitude of a vector is calculated using the Pythagorean theorem, which states that the magnitude (M) of a vector with components x and y is equal to the square root of the sum of the squares of its components (M = √(x2 + y2)).
The direction of a vector is usually represented by an angle (θ) measured in degrees or radians. This angle is measured counterclockwise from the positive x-axis to the vector.
No, a vector cannot have a negative magnitude. Magnitude is a scalar quantity, which means it only represents the size of the vector and does not have a direction. A negative magnitude would imply that the vector has a direction opposite to the one specified.
Even if two vectors have the same magnitude and direction, they can still be different if they have different starting points. This is because a vector represents a displacement or movement from its starting point to its end point. Therefore, two vectors with the same magnitude and direction but different starting points will have different end points and thus be different vectors.