Velocity of fluid through a point on a plane

[racnna]

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

 

[tiny-tim]

hi 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] …

but what is the relevance of the position vector?

 

[racnna]

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?

 

[tiny-tim]

yup!

 

[Nickie]

.I would suggest that you check your calculation again to ensure that you have correctly calculated the dot product and used the correct units. If you are still getting a negative velocity, it could be due to the orientation of the plane and the direction of the flow. You may need to consider the direction of the normal vector of the plane and the direction of the velocity vector to determine the actual speed at which the fluid is passing through the plane. Additionally, it may be helpful to draw a diagram to visualize the situation and better understand the direction and magnitude of the velocity at the given point.