Parallel vectors6/18/2023 ![]() Using the definition of the dot product of vectors, we have, Let us assume two vectors, v and w, which are parallel. The dot product of the vector is calculated by taking the product of the magnitudes of both vectors. In the above one where v = bw, (‘b’ is a scalar) v and w are in the same direction if b > 0, i.e., the scalar is positive, and both the vectors v and w are in opposite directions if b < 0, that is the scalar is negative. Two vectors v and w are parallel to each other if v = bw, where ‘b’ is a scalar. That means we can have more than two vectors.Īny vector a is always parallel to itself, i.e., a is always parallel to a. Collinear vector means that the two parallel vectors are always parallel to the same line, but they may or may not be in the same direction. Parallel vectors are sometimes known as a set of collinear vectors. Now, these two vectors are always parallel to each other. The parallel vectors are vectors that are in the same direction or exactly the opposite direction, which means if we have any vector v, which is one vector, its opposite vector will be -v. Another way to say it is: Two vectors a and b are called parallel if and only if the angle they form between them is zero degrees or 0°.Ī pictorial representation of the parallel vector, which is in the same direction, is given in Figure I:Ī pictorial representation of the parallel vector, which is in opposite directions, is given in Figure II:Ī pictorial representation of non-parallel vectors, i.e., vectors that are not parallel, is given below in Figure III: Two vectors a and b are called parallel if the angle they form from the vertical axis or the horizontal axis (not necessarily together) is the same or equal.
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