He might use a quantity vector, to represent the quantity of fruit he sold that day.

On a given day, he sells 30 apples, 12 bananas, and 18 oranges. For example, suppose a fruit vendor sells apples, bananas, and oranges. However, vectors are often used in more abstract ways. So far, we have focused mainly on vectors related to force, movement, and position in three-dimensional physical space. In (Figure), the direction cosines of are and The direction angles of v are and Angle γ is formed by vector v and unit vector k. Angle β is formed by vector v and unit vector j. It even provides a simple test to determine whether two vectors meet at a right angle.Īngle α is formed by vector v and unit vector i. The dot product can also help us measure the angle formed by a pair of vectors and the position of a vector relative to the coordinate axes. The dot product essentially tells us how much of the force vector is applied in the direction of the motion vector. In this section, we develop an operation called the dot product, which allows us to calculate work in the case when the force vector and the motion vector have different directions.

In this chapter, however, we have seen that both force and the motion of an object can be represented by vectors. Under those conditions, work can be expressed as the product of the force acting on an object and the distance the object moves. In Introduction to Applications of Integration on integration applications, we looked at a constant force and we assumed the force was applied in the direction of motion of the object.

If we apply a force to an object so that the object moves, we say that work is done by the force. Calculate the work done by a given force.Explain what is meant by the vector projection of one vector onto another vector, and describe how to compute it.Find the direction cosines of a given vector.Determine whether two given vectors are perpendicular.Calculate the dot product of two given vectors.

Dot product in microsoft word equation