Vectors that lie in the parallel line or the same line concerning their magnitude and direction are known to be collinear vectors, also known as parallel vectors. Three or more vectors lying in the same plane are known as coplanar vec The vectors having the same directions are said to be like vectors whereas vectors having opposite directions are said to be unlike vectors. Let us consider O is taken as reference origin and X is an arbitrary point in the plane then the vector is called the position vector of the point.Ī vector is said to be a co-initial vector when two or more vectors have the same starting point, for example, Vectors AB and AC are called co-initial vectors because they have the same starting point A. Let OX be a point in a plane concerning its origin. Point X taken in the plane is said to be a position vector. But two-unit vectors cannot be equal as they might have different directions. Suppose if x is a vector having a magnitude x then the unit vector is denoted by x̂ in the direction of the vector, and it has a magnitude equal to 1. The zero vector doesn’t have any specific direction.Ī vector is said to be a unit vector when the magnitude of the vector is 1 unit in length. For instance, PQ is a line segment the coordinates of the point P are the same as that of the point Q. The 10 types of vectors are:Ī vector is said to be a Zero Vector when the magnitude of the vector is zero and the starting point and the endpoint of the vector is the same. There are commonly 10 different types of vectors frequently used in maths. Here we will be discussing different types of vectors. In addition, the dot product and the cross product are two methods for multiplying two vectors together. Addition, subtraction, and multiplication by a scalar are the vector operations. Some basic vector operations can be done geometrically without the use of a coordinate system. Vectors describe how an object moves from one location to the other. The initial point of a vector is also known as the tail, while the terminal or endpoint is known as the head. Vectors can also be defined by their initial and terminal points, which can indicate by an arrow above them. Vectors are normally represented by a bold lowercase letter, such as a, or by an arrow over the letter. An increase and decrease in temperature are the best examples of a vector, it has both magnitude and direction. The start point is its tail, and the endpoint is its head. In a line, the length of a line is a magnitude, and the arrow is its direction. A vector is a geometrical entity that has magnitude and direction. Or by scalar multiplication by a zero scalar.To recall, in Mathematics a physical quantity that has both magnitude and a direction is said to be a vector. Clearly, null vectors are formed due to the resultant of two or more vectors in different directions. We can also say that a null vector is a point with no direction or magnitude, thus we can represent a null vector by a point in a 3D space. Similarly, a null vector can also be formed, when a zero scalar is multiplied with a non-zero vector, then from scalar multiplication, we can say that the resultant vector formed will be a null vector, with magnitude zero, and no direction.Īn example would be work done by women standing at the same place, by holding a basket over her head. This null vector will have zero magnitude and no direction.Ī real life example would be, two people pushing the cars in opposite directions with the same or equal force, or two people pulling a rope from opposite sides with the same or equal forces. Then, clearly, we can say that when two vectors of same magnitude and opposite direction act on the same body, then the resultant of the two vectors will be a null vector. We also know that the direction of this resultant vector, formed due to vector addition is given by the phase diagram. We also know that two vectors can be added by vector addition. We know that mathematical operations like addition, subtraction, multiplication and division can be carried out on vectors. The null vector can be formed due to various cases as discussed below. Then, such a vector is called a null vector. Thus clearly vectors can also have a value like zero. Hint: We know that a vector is a physical quantity which has both magnitude and direction.
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