Tuesday, October 14, 2014

Scalar Product and Vector Product of Vectors

Vector multiplication has two possibilities. If two vectors are multiplied and the resultant is a scalar,then that kind of a product is called scalar product. While you’re measuring  the scalar product we have to multiply one vector  with the component of the other vector that is acting along the direction of the first vector.

If if two vectors are perpendicular to each other then their  scalar product is null.Basing on this concept we can solve some problems and identify the unknown value when it is given as a condition the problem that the two vectors are perpendicular to each other.

Work done is a simple example of a scalar product which is a product of both force and displacement. It is a scalar because the product of them is not going to have direction but only a magnitude.



Vector product:

If two vectors are multiplied and the resultant is a vector then that kind of a product is called as cross product. The output of this product is not only going to have magnitude and direction and is also going to satisfy the laws.To find a direction of this vector are we can use cork Screw rule or right hand thumb rule.



As per the corkscrew rule, if the head of the screwy is rotating from one vector to other, their cross product  vector is going to move along the direction of the tip of the screw  who is the perpendicular plane of these two vectors.



We can find the value of the cross product using the mathematical Matrix Method has shown.



We can find the area of parallelogram and area of the triangle using the cross product as shown.



Moment of the force can be expressed as a cross product of force and the perpendicular distance. We can explain in detail that how it is going to be a cross product of two vectors are shown below.



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