Let us have a better understanding of the concept with the help of an example.Ĭalculate the magnitude of the following 3-D vectors. Only the magnitude of the null vector is zero. The magnitude of a vector is always positive, as the common mistake in computing the magnitude of a vector is that we forget the absolute sign. Where u x, u y, and u z are the magnitudes of coordinate axes.Īs we have already discussed, the concept of a 3-D vector is not different from that of a 2-D vector, except now there is one more dimension in the 3-D vector. The magnitude of 3-D vectors is calculated in a similar way with the addition of one more coordinate. How To Find The Magnitude Of A 3-D Vector? A 3-D vector can be represented as u (u x, u y, u z ) or or u x i + u y j + u z k. Each pair forms a plane, xy-plane, yz-plane, and xz-plane. There are three axes now, so this means that there are three intersecting pairs of axes. ![]() ![]() Such a system is called a 3-dimensional rectangular coordinate system.Ī vector drawn in a 3-D plane and has three coordinate points is stated as a 3-D vector. Now, the first question is, “What is a 3-D coordinate system?” A 3-D coordinate system has 3 dimensions or can be regarded as having 3 perpendicular axes: x, y, and z-axes. We can do various computations like finding the angle between two vectors, scalar multiplications, etc. 3-D vector operations are analogous to 2-D operations with just an added computational step. That’s why it is necessary to understand the concept of 3-D vectors in a 3-D coordinate system and their properties.Ī 3-D vector is like a 2-D vector in all aspects, but in the case of a 3-D vector, we need to keep track of one more direction. Still, if we need to specify various landscapes and environments, only a 2-D description of a map is not enough. Similarly, if we consider a map in 2-D, it’s only useful for navigating from one point to another. So, to describe the impact of all the features, we need to use three-dimensional space. To avoid the computational complexity and simplify the idea so that we can understand the concept easily, it’s time to learn about 3-D vectors.įor example, if we need to specify the direction of any rigid object or body such as cars, airplanes, robots, etc., one would normally think that he needs three coordinates to define the position of the objects x, y, and z-axis and that is completely correct. How to calculate the angle between two 3-D vectors?Ī 3-D vector is a vector represented in a 3-D plane having three coordinates x, y, and z.Īs in the previous sections, we have learned and discussed the vectors in 2-dimensional space. ![]()
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