Tuesday, February 21, 2017

Vector resolution and Laws of Vectors Video lesson

We are here discussing regarding the introduction of vectors, resolution of vectors and laws of vectors. Vector is a physical quantity that has magnitude, direction and satisfy the laws of vector algebra. Some physical quantities in physics need both magnitude and direction to explain them completely and that kind of vectors are treated as vectors. Simple examples of vectors are displacement,velocity,momentum,force and torque.

Vectors are graphically represented as an arrows and the head of the arrow is treated as its direction. The size of the arrow is directly proportional to the magnitude of the vector. The direction of the vector is identified with its unit vector and it has only direction of the vector and the magnitude of the unit vector is one unit only. Thus any vector can be represented as the product of magnitude of the vector and its unit vector.

The direction of the vector are represented as unit vectors i,j and k along X,Y and Z axis. All of they are having a magnitude of one unit. If two vectors are having same magnitude and same direction then the two vectors are called unit vectors. If their magnitude is same but the direction is opposite, then one vector is called negative vector of the other vector and vice versa. Here is a video lesson on the basics of the vectors.

Resolution of the vector

A vector could be only along one direction and then identifying the direction is easy like it is along X or Y axis. If any vector is in a plane making some angle with any of the axis, then we can not say that it is either along the X or Y axis. To know how much part of the given vector is along the given axis, we can resolve the vector into components. A component is a part of a given vector along a specified direction and we use trigonometry  to resolve the vector into components. If we add the two vectors, we will get back the original vector without any loss. It is explained in the video lesson as shown in the diagram below.

Laws of vectors

Vectors addition and subtraction can be done either graphically or algebraically. For graphical addition or subtraction, we are going to shift the given and required vector parallel. As shifting the vector in parallel  won't change either its magnitude or direction, the vector remains same. Any way this can be done with much ease using mathematical tools. Vector addition satisfies commutative law, and distributive law. But vector subtraction does not satisfy the commutative law. It is explained as shown in the video lesson below.

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