1. A vector P having a magnitude of 676 Newton  is directed from A(2,3,5) to B(-1,2,4) while another vector F has a magnitude of 1352 Newton is directed from A to D(0,3,6). Find the following:|
a. ) Dot product (P dot F)
b. ) Component of the vector P along the line AC if C is at (4,5,-3)
c.) Component of vector F along the line AC

To solve this problem, we need to find vectors \( \mathbf{P} \), \( \mathbf{F} \), and the unit vector along \( \mathbf{AC} \), and then compute the dot product and components as requested.

### Step-by-step Solution:

1. **Find Vectors \( \mathbf{P} \) and \( \mathbf{F} \):**

   Vector \(

Explore a vector analysis problem involving dot product and vector components. Learn how to compute the dot product of vectors P and F, and find the components of vector P and F along line AC. Suitable for high school students studying vector algebra.

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