Velocity of fluid through a spherical surface

[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?? i did this and got a negative velocity! HELP

 

[Chestermiller]

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?? i did this and got a negative velocity! HELP

The volumetric flux of fluid (volume per unit area = normal component of velocity) is equal to the velocity dotted with a unit normal to the plane.