Vector Projection Problem: Solving for Component in Given Direction

[Allenman]

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

\vec{F} = (70.0 \hat{i} + F_{y} \hat{j} + 140.0 \hat{k} ) N​

has a component of +20.0 N in the direction defined by the vector

\vec{P} = (6 \hat{i} - 3 \hat{j} - 2 \hat{k} ) kN​

Solve for F_{y}.

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 \vec{F} is in the \vec{P} 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?

 

[gneill]

The problem makes sense. When you want to know the projection of one vector onto another, what vector operation comes to mind?

 

[Allenman]

Wow... I didn't recognize it as a vector projection problem... Thank you!