Vector Projection Problem: Solving for Component in Given Direction

In summary, the question on the CEE 270 exam involves finding the component of a force vector in the direction defined by another vector. The attempt at a solution includes confusion about whether or not to rotate the coordinate system, but the professor clarifies that no rotation is necessary. The solution involves using vector projection.
  • #1
Allenman
58
0
This question was just given on a CEE 270 exam (handwritten by professor). The way it's written doesn't make any sense to me.

Homework Statement



A force vector
[itex]\vec{F}[/itex] = ([itex]70.0 \hat{i} + F_{y} \hat{j} + 140.0 \hat{k}[/itex] ) N​

has a component of +20.0 N in the direction defined by the vector
[itex]\vec{P}[/itex] = ([itex]6 \hat{i} - 3 \hat{j} - 2 \hat{k}[/itex] ) kN​

Solve for [itex]F_{y}[/itex].

The Attempt at a Solution



I asked the professor if I needed to rotate the coordinate system as the question states that a component of [itex]\vec{F}[/itex] is in the [itex]\vec{P}[/itex] direction. He said no rotation of the coordinate system should be needed.

I am very confused at how to even approach this problem. Please help. Does it even make sense?
 
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  • #2
The problem makes sense. When you want to know the projection of one vector onto another, what vector operation comes to mind?
 
  • #3
Wow... I didn't recognize it as a vector projection problem... Thank you!
 

What are vector components?

Vector components are the individual parts of a vector that represent its magnitude and direction in a specific coordinate system. They are usually denoted by their horizontal and vertical values, often referred to as x and y components.

How do you find the components of a vector?

The components of a vector can be found using trigonometric functions and the Pythagorean theorem. The x component is determined by multiplying the vector's magnitude by the cosine of the angle it makes with the x-axis. Similarly, the y component is found by multiplying the magnitude by the sine of the angle. The Pythagorean theorem can then be used to find the overall magnitude of the vector.

What is the difference between vector components and vector resolution?

Vector components are the horizontal and vertical parts of a vector, while vector resolution is the process of breaking down a vector into its components. Essentially, vector components are the result of vector resolution.

Can vector components be negative?

Yes, vector components can be negative. This indicates that the vector is pointing in the opposite direction of the positive axis. For example, a vector with an x component of -5 would be pointing to the left on a standard coordinate plane.

How are vector components used in physics?

Vector components are used in physics to break down forces and motion into their horizontal and vertical components. This allows for more accurate calculations and predictions of the overall motion of an object. In addition, vector components are used to analyze the equilibrium of forces in systems, as well as in the calculation of work and energy.

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