Induction is a mathematical method of proving statements about a set of numbers by using a specific set of base cases and a general rule to show that the statement holds for all numbers in that set.
Congruence is a mathematical concept that describes the relationship between two objects that have the same shape and size. In geometry, this is often shown by using congruent figures that have the same measurements for all corresponding sides and angles.
Vectors are mathematical quantities that have both magnitude and direction. They are often represented graphically as arrows and can be used to describe physical quantities such as displacement, velocity, and force.
Vectors have many practical applications in fields such as physics, engineering, and navigation. They can be used to model and solve problems involving forces, motion, and direction. For example, vectors can be used to calculate the trajectory of a projectile or the displacement of an object.
Some common properties of vectors include commutativity, where the order of vector addition does not affect the result, and associativity, where the grouping of vectors in an addition or multiplication does not affect the result. Vectors also have a magnitude and direction, and they can be multiplied by a scalar to change their magnitude without changing their direction.