![]() Given the vector P = (2, 4), determine the negative of P.īy definition, the negative of a vector has the same magnitude as the reference vector’s opposite direction. We will then discuss some more examples and their step-by-step solutions to develop an even deeper understanding of negative vectors. This section will first consider different examples where we find negative vectors by comparing the reference vector’s components. Remember that the magnitude of vector – X is the same as that of vector X. To obtain X’s negative vector, we multiply X by -1, making it – X. Two such vectors will be the negative vectors of each other.įinding the negative vector of a given vector can be done by placing a negative sign in front of it. The basic idea behind finding the negative vector of a given vector is to find the two components of the given vector (i.e., the vector’s magnitude and the direction) and then find a vector of the same length that points in the opposite direction. This criterion is enough to show that B is the negative vector of A and vice versa. We say that the vector B is the negative of vector A, or: For example, consider the vectors A = (ax1, ay1) and B = (bx1, by1). If the vectors’ coordinates are equal in value but have opposite signs, the vectors will be the negatives of each other. ![]() Mathematically, we can say that two vectors A and B are the negatives of each other if they satisfy the following two conditions:Ī = – B (“Vector B is negative of vector A”)Ī ↑ and B ↓ or A↓ and B ↑ (Opposite directions).Īnother simple method to find out if two vectors are the negatives of each other is to compare their coordinates. The negative sign is used here to indicate that the vector has the opposite direction of the reference vector. The magnitude, or length, of a vector, cannot be negative it can be either be zero or positive. It is important to note that the vector PQ and the vector QP have the same magnitude but opposite directions, making them the negative vectors of each other. That is, QP is the negative vector for PQ, as depicted in the image below. Since these directions are opposite, we say that PQ = – QP. Vectors are only negative with respect to another vector.įor example, if a vector PQ points from left to right, then the vector QP will point from right to left. A negative sign will reverse the direction of a vector and make it a negative vector. Vectors having the same length as a particular vector but in the opposite direction are called negative vectors. In this article, we will discuss the following subtopics related to negative vectors: “A vector whose magnitude is the same as that of the reference vector, but its direction is opposite to that of the reference vector.” If there are negative scalars, is it also possible to have a negative vector? It is! In fact, a negative vector is: Negative Vectors – Explanation & Examples
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