1. Adding Vectors that are not perpendicular
Holt Physics
Chapter 3 Section 2 (continued)

2. Non-perpendicular vectors
Because vectors do not always form right triangles, you cannot automatically apply the Pythagorean theorem and tangent function to the original vectors
Vector 2
Resultant vector
No right triangle!
Vector 1

3. Non-perpendicular vectors
This will require new “old” variables
For Displacement Vectors
Vector # Vector #2 Resultant
Δx1 Δx2 ΔxT
Δy1 Δy2 ΔyT
DR1 DR2 DRT
θ1 θ2 θR

4. Non-perpendicular vectors
Step #1
You must resolve vector #1 into x & y components
Vector 1
DR1
Δy1 θ1
Δx1

5. Non-perpendicular vectors
Step #2
You must resolve vector #2 into x & y components
DR2
Δy2
Vector 2
Δx2 θ2

6. Non-perpendicular vectors
Step #3
Add all X components to find ΔxT
Δx1 + Δx2 = ΔxT
Δx1
Δx2
ΔxT

7. Non-perpendicular vectors
Step #4
Add all Y components to find ΔyT
Δy1 + Δy2 = ΔyT
Δy2
ΔyT
Δy1

8. Non-perpendicular vectors
Step #5
Now you have total x & y components
Use Pythagorean theorem to find resultant
DRT2 = ΔxT2 + ΔyT2
DRT
ΔyT
ΔxT θR

9. Non-perpendicular vectors
Step #6
Use tangent to find the angle
- Same equations -
Tan θR = ΔyT  θR = Tan-1 (ΔyT / ΔxT)
ΔxT

10. Non-perpendicular vectors
You may wish to draw the x-total and y-total vectors into the original drawing if it helps you, or make a new triangle with just the totals.
Vector 2
Resultant vector
DRT
Vector 1
ΔyT θR
ΔxT

11. Non-perpendicular vectors
* If you have velocities instead of displacement:
 Replace “Δ” and “D” with “V”
* If you have more than two vectors, the third vector’s variables will be “Δx3, ….”, and so on.