To find the magnitude of the resultant vector when adding vectors $a + b + c$, we need to resolve each vector into its components and then add them accordingly.

Step 1: Resolve each vector into components

• Vector $a$: Magnitude = 25 N, Angle = $0^\circ$

  • $a_x = 25 \cos(0^\circ) = 25$ N
  • $a_y = 25 \sin(0^\circ) = 0$ N

• Vector $b$: Magnitude = 35 N, Angle = $180^\circ$

  • $b_x = 35 \cos(180^\circ) = -35$ N
  • $b_y = 35 \sin(180^\circ) = 0$ N

• Vector $c$: Magnitude = 20 N, Angle = $270^\circ$

  • $c_x = 20 \cos(270^\circ) = 0$ N
  • $c_y = 20 \sin(270^\circ) = -20$ N

Step 2: Sum the components

Now we add the corresponding components for the total vector:

• $R_x = a_x + b_x + c_x = 25 + (-35) + 0 = -10$ N
• $R_y = a_y + b_y + c_y = 0 + 0 + (-20) = -20$ N

Step 3: Calculate the magnitude of the resultant vector

The magnitude of the resultant vector $R$ is given by: $|R| = \sqrt{R_x^2 + R_y^2}$ Substituting the values: $|R| = \sqrt{(-10)^2 + (-20)^2} = \sqrt{100 + 400} = \sqrt{500} \approx 22.36 \, \text{N}$

Conclusion:

The magnitude of the resultant vector is approximately 22.36 N.

Would you like more details on this calculation or any further questions?

---

Here are 5 related questions:

1. How do you determine the direction of the resultant vector?
2. What are vector components, and why are they important?
3. How do you calculate the angle of a resultant vector?
4. What happens if two vectors have the same magnitude but opposite directions?
5. How do you add vectors graphically?

Tip: Always resolve vectors into components to simplify addition!