Thursday, March 2, 2017

Dot Product and Cross Product of Vectors Video Lesson

Dot product and cross product of two vectors is a way of multiplication of the vectors.Vector is a physical quantity that has both magnitude and direction and satisfies the vector algebra. Some physical quantities demands both magnitude and direction with out which we cannot explain the physical quantity. Vector has to be added to the other vectors  but we can not add one vector with the other vector. Vector subtraction also follows the same rules of vector addition with the concept of negative vector. 

Vector quantity can be multiplied with a scalar also and the resultant is a vector with the same magnitude of the given vector. A vector can be multiplied with a vector and the resultant can be a scalar or vector. If two vectors are multiplied and the product is a scalar and that kind of multiplication is called scalar product or dot product of two vectors. To get the dot product of two three dimensional vectors, we shall multiply the corresponding components and add all of them.  A video lesson is given below to explain the dot product as shown in the diagram below.

Work done as dot product

We know  that work is said to be done when applied force is able to produce some displacement. When we apply some force at some angle on a body  on a horizontal surface. The total force is not acting along the horizontal surface and only a component of force is acting along the horizontal. To know that value, we need to resolve the force vector into components. The component of the force acting along the direction of the displacement is producing the displacement and the other component has no impact on the displacement. Thus we need to consider only a component of force and that shall be multiplied with the displacement to get the work done. It is explained as the dot product of force and displacement as shown in the video lesson below.

Cross Product of two vectors

If we multiply one vector with another vector and the resultant of the product is a vector then the kind of vector product is called cross product of the given vectors. The resultant will have not only magnitude and also has the direction. To find the cross product of two vectors of two vectors, we need to multiply the cross product of unit vectors and get the resultant of two unit vectors also a unit vector but having the different direction. To get the direction of cross product of the two vectors we need to use right hand thumb rule or cork screw rule as explained in the video lesson below.

Torque as the cross product of two vectors

Torque means the turning effect and it is a physical quantity useful in understanding the rotational motion of a body. We shall apply a force away from axis of rotation. We know that the rotating particle is at a distance from the axis of rotation. Applied force and the perpendicular distance from the axis of rotation both are vectors. The resultant of two vectors product is also a vector and we can find the torque as shown in the video lesson below.

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