# Velocity of fluid through a point on a plane

• racnna
In summary, the problem is asking for the speed at which fluid passes through a plane at point P, which has coordinates (1,2,4). To find this, you can take the dot product of the velocity vector and the normal unit vector of the plane, which is given by the vector b=-i+2k. The point P is not needed to compute the flow through the plane, as the velocity and normal vectors are already given.

#### racnna

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] 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?

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What are you trying to determine?

so sorry. i forgot to type the actual question lol. I've edited my post. I am trying to determine the speed at which the fluid passes through the plane

This is the projection of the velocity on the normal to the plane. Which you could obtain as a scalar product of the velocity vector and the normal unit vector. Note the normal vector given is not unit.

yes. but how doe the point P come into play?

b/|b| gives the unit vector normal to the plane right?
how about P? what do i do with it?

You are explicitly given a velocity vector at P. You are explicitly given a normal vector of a plane passing through P. That's all you need to compute the flow through the plane at P. Given what you are given, there is no (more) dependence on the coordinates of P.

Ok.

my first thought was to just dot v with the normal unit vector of the plane...but then i noticed they gave me specific coordinates of the point and i felt i had to do SOMETHING with it...hmm..