Homework Help: Finding parallel and perpendicular components of a force

1. Oct 8, 2012

Poto23

1. The problem statement, all variables and given/known data
Consider a plane with the outer normal unit vector of (1/√2, -1√2, 0). There is a force of (2,1,5) acting on the surface. What is the component of force normal and parallel to the plane? What is the maximum parallel component to the plane?

I would like to check my answers for the first two, but do not know how to find the maximum parallel component. I'm guessing since my direction is at a 45 degree angel, the maximum parallel component of the force should be given at the 45 degree angle?

2. Relevant equations
Dot product and Pythagorean theorem
Force = 2^2 +1^2 + 5^2 = √30

3. The attempt at a solution
I found the normal force to be (1/2, -1/2, 0) through doing the dot product of force and the unit vector, and then multiplying the scalar product by the unit vector again.
For the parallel component, I found the magnitude of the Force and the magnitude of the normal Force, and used Pythagorean theorem. I got √Force^2 - 1^2. = 29.98(1/√2, 1/√2, 0).

Thank you

2. Oct 9, 2012

bump 10char

3. Oct 9, 2012

HallsofIvy

Your normal vector is correct. To find the parallel vector, just use the fact that the normal and parallel vector must add to the original vector: (x, y, z)+ (1/2, -1/2, 0)= (2, 1, 5).

4. Oct 9, 2012

Poto23

I will wait next time. Thank you for letting me know.