Find the Coordinates/Magnitude of projection of two vectors

In summary, the question asks to find the coordinates and magnitude of the projection of vector u→ onto vector v→. The magnitude can be found by squaring each component of the projection vector, adding them, and taking the square root. The magnitude is √72.
  • #1
Physics345
250
23

Homework Statement



Given two vectors u→=(16,5,2) and v→=(3,−2,−2) find the following:
  1. The coordinates of the projection of u→ on v→
  2. The magnitude of the projection of u→ on v→
    .

Homework Equations

The Attempt at a Solution


I have never done a question like this before, I was curious did I do it correctly? If not should I instead find the projection from point A to B?
Here's my attempt: (I wrote it out in word to make it easier to read)
P3BkGLn.png
 

Attachments

  • P3BkGLn.png
    P3BkGLn.png
    9.6 KB · Views: 541
Last edited:
Physics news on Phys.org
  • #2
(a) is correct. For (b) you need to work out the magnitude of the vector that is the answer to (a). Square each component, add, then take the square root. The answer will be more than 2.
 
  • Like
Likes Physics345
  • #3
andrewkirk said:
(a) is correct. For (b) you need to work out the magnitude of the vector that is the answer to (a). Square each component, add, then take the square root. The answer will be more than 2.
Oh wow That's all they want me to do I've been doing that I assumed this was asking me to do something else because it's asking for "Magnitude of the projection". I assumed it was different. Anyways I appreciate it, thanks for pointing that out to me.
 
  • #4
=√(6)^2 +(-4)^2 +(-4)^2
=√72

Therefore,the magnitude of u ⃗ on v ⃗ is √72

Thanks again =)
 

Related to Find the Coordinates/Magnitude of projection of two vectors

What is the definition of projection of two vectors?

The projection of two vectors is the component of one vector that lies in the direction of the other vector. It is also known as the scalar projection or the dot product of the two vectors.

How do you find the coordinates of the projection of two vectors?

To find the coordinates of the projection of two vectors, you first need to calculate the dot product of the two vectors. Then, divide the dot product by the magnitude of the second vector to get the magnitude of the projection. Finally, multiply the magnitude with the unit vector of the second vector to get the coordinates of the projection.

What is the significance of finding the projection of two vectors?

Finding the projection of two vectors is useful in many applications, such as in physics, engineering, and computer graphics. It can be used to determine the amount of force acting in a particular direction, the amount of work done in a specific direction, and to create 3D projections of objects.

Can the projection of two vectors be negative?

Yes, the projection of two vectors can be negative. This happens when the angle between the two vectors is greater than 90 degrees, and the projection is in the opposite direction of the second vector.

Can the projection of two vectors be greater than the magnitude of the second vector?

No, the projection of two vectors cannot be greater than the magnitude of the second vector. The magnitude of the projection is always less than or equal to the magnitude of the second vector.

Similar threads

  • Calculus and Beyond Homework Help
Replies
1
Views
2K
  • Calculus and Beyond Homework Help
Replies
1
Views
810
  • Calculus and Beyond Homework Help
Replies
7
Views
508
  • Calculus and Beyond Homework Help
Replies
6
Views
2K
  • Calculus and Beyond Homework Help
Replies
1
Views
1K
  • Calculus and Beyond Homework Help
Replies
2
Views
1K
Replies
5
Views
1K
  • Calculus and Beyond Homework Help
Replies
1
Views
1K
  • Calculus and Beyond Homework Help
Replies
1
Views
648
  • Calculus and Beyond Homework Help
Replies
2
Views
1K
Back
Top