# Find the Coordinates/Magnitude of projection of two vectors

• Physics345
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.
Physics345

## 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→
.

## 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)

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(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.

Physics345
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.

=√(6)^2 +(-4)^2 +(-4)^2
=√72

Therefore,the magnitude of u ⃗ on v ⃗ is √72

Thanks again =)

## 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.

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