A vector is an object that has both a magnitude and a direction. Two examples of vectors are those that represent force and velocity. Both force and velocity are in a particular direction. The magnitude of the vector would indicate the strength of the force or the speed associated with the velocity.

Vectors are used in science to describe anything that has both a direction and a magnitude. They are usually drawn as pointed arrows, the length of which represents the vector’s magnitude.

A vector is a quantity or phenomenon that has two independent properties: magnitude and direction. The term also denotes the mathematical or geometrical representation of such a quantity. Examples of vectors in nature are velocity, momentum, force, electromagnetic fields, and weight.

A vector describes a movement from one point to another. A vector quantity has both direction and magnitude (size). A scalar quantity has only magnitude. A vector can be represented by a line segment labelled with an arrow. Vectors are equal if they have the same magnitude and direction regardless of where they are.

Its length is its magnitude, and its direction is indicated by the direction of the arrow. The vector here can be written OQ (bold print) or OQ with an arrow above it. Its magnitude (or length) is written OQ (absolute value symbols). A vector may be located in a rectangular coordinate system, as is illustrated here.

Most commonly in physics, vectors are used to represent displacement, velocity, and acceleration. Vectors are a combination of magnitude and direction, and are drawn as arrows. The length represents the magnitude and the direction of that quantity is the direction in which the vector is pointing.

One type, the dot product, is a scalar product; the result of the dot product of two vectors is a scalar. The other type, called the cross product, is a vector product since it yields another vector rather than a scalar.

The cross product of two parallel vectors is a zero vector (i.e. 0 ).

The right hand rule for cross multiplication relates the direction of the two vectors with the direction of their product. Since cross multiplication is not commutative, the order of operations is important.

The direction of the vector (A crossB) is defined by the so-called right-hand rule. Using the fingers of the right hand pointed in the direction of A, the fingers are rotated into the vector B(remember – the smaller of the two possible angles).

The cross product of two vectors does not obey commutative law. The cross product of two vectors are additive inverse of each other.

The law states that the sum of vectors remains same irrespective of their order or grouping in which they are arranged. This fact is known as the ASSOCIATIVE LAW OF VECTOR ADDITION.

Vector, in physics, a quantity that has both magnitude and direction. It is typically represented by an arrow whose direction is the same as that of the quantity and whose length is proportional to the quantity’s magnitude. Although a vector has magnitude and direction, it does not have position.

By definition, two vectors are equal if and only if they have the same magnitude in the same direction. It can be seen from the figure that vector a and vector b are parallel and pointing in the same direction, but their magnitudes are not equal. Thus, we can conclude that the given vectors are not equal.

When we want to find out a vector of magnitude equal to that of the given scalar , and direction is same as that of a given unit vector , we multiply the scalar to the unit vector . Example : Suppose I want to denote a force acting along the positive direction of the x-axis .

Vectors have many real-life applications, including situations involving force or velocity. For example, consider the forces acting on a boat crossing a river. The boat’s motor generates a force in one direction, and the current of the river generates a force in another direction. Both forces are vectors.