Ev(Unit Vector) and projection of a vector in a dot product

In summary, the equations for w are w=(u.ev)ev or w=( (u.v)/(v.v) )v. The second equation is easier to understand if we understand the first one, and ev represents the unit vector. The reason for the extra ev in the equation is to define the direction of w, as (u.ev) is a scalar and does not change the direction of w.
  • #1
Usernam
2
0
So my book says

Lets suppose,

We have two vector v and u

w=projection of u ev= unit vector θ=angle between the two

w=(u.ev)ev or w=( (u.v)/(v.v) )v

Now, the second equation is fairly easy to understand if we understand the first one because ev= v / |v|

What is bothering me is I have no idea why w=(u.ev)ev.

It would be more reasonable, as per me, if w=(u.ev)

But that is not the case.

Why is that extra ev lingering around in the equation.

ANY IDEAS?
 
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  • #2
w is a vector parallel to ev. (u.ev) is a scalar (± length of w), so you need the entire expression to define the vector w.
 

What is an Ev(Unit Vector)?

An Ev(Unit Vector) is a vector with a magnitude of 1 and a direction that is parallel to the original vector. It is used to represent the direction of a vector without changing its magnitude.

How is an Ev(Unit Vector) calculated?

To calculate an Ev(Unit Vector), divide each component of the original vector by its magnitude. This will result in a vector with a magnitude of 1 and the same direction as the original vector.

What is the dot product of two vectors?

The dot product of two vectors is a scalar quantity that is calculated by multiplying the magnitudes of the two vectors and the cosine of the angle between them. It is used to determine the relationship between two vectors, such as if they are perpendicular or parallel.

How is the projection of a vector calculated?

The projection of a vector onto another vector is calculated by taking the dot product of the two vectors and dividing it by the magnitude of the vector onto which the projection is being made. This will result in a scalar quantity that represents the length of the projection.

What is the significance of the dot product in physics and engineering?

The dot product has many applications in physics and engineering, such as determining work done by a force, finding the angle between two vectors, and calculating the magnitude of a vector in a specific direction. It is also used in vector calculus and is essential in many mathematical models and equations.

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