Velocity of fluid through a point on a plane

AI Thread Summary
The discussion focuses on calculating the speed of fluid passing through a plane normal to a given vector at a specific point. The fluid's velocity is given as 2i - 3j m/s at point P with coordinates (1,2,4). Participants suggest using the dot product of the fluid velocity vector and a unit normal vector of the plane to find the speed. There is some confusion about the relevance of the position vector, which is ultimately deemed unnecessary for the calculation. The consensus is to focus on the dot product of the velocity and the normal vector to determine the fluid's speed through the plane.
racnna
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Homework Statement



Fluid flows with velocity 2i - 3j m/s at point P having coordinates (1,2,4). Consider a plane through P which is normal to the vector b=-i+2k. What is the speed at which the fluid passes through the plane?

The Attempt at a Solution


Should I do the dot product of the position vector P=[1,2,4] and b vector, then multiply this by unit vector that is in the direction of the b vector, and then dot the result with the velocity vector?

thats what i did but I am getting a negative velocity
 
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hi racnna! :smile:
racnna said:
Fluid flows with velocity 2i - 3j m/s at point P having coordinates (1,2,4). Consider a plane through P which is normal to the vector b=-i+2k. What is the speed at which the fluid passes through the plane?
…
Should I do the dot product of the position vector P=[1,2,4] …

but what is the relevance of the position vector? :confused:
 
hmm...maybe i don't need it?? ok just ignore the position vector part...

should i just find the dot product of v and a unit normal vector of the plane?
 
yup! :biggrin:
 

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