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**Adding Vectors that are not perpendicular**

Holt Physics Chapter 3 Section 2 (continued)

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**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

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**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

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**Non-perpendicular vectors**

Step #1 You must resolve vector #1 into x & y components Vector 1 DR1 Δy1 θ1 Δx1

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**Non-perpendicular vectors**

Step #2 You must resolve vector #2 into x & y components DR2 Δy2 Vector 2 Δx2 θ2

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**Non-perpendicular vectors**

Step #3 Add all X components to find ΔxT Δx1 + Δx2 = ΔxT Δx1 Δx2 ΔxT

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**Non-perpendicular vectors**

Step #4 Add all Y components to find ΔyT Δy1 + Δy2 = ΔyT Δy2 ΔyT Δy1

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**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

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**Non-perpendicular vectors**

Step #6 Use tangent to find the angle - Same equations - Tan θR = ΔyT θR = Tan-1 (ΔyT / ΔxT) ΔxT

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**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

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**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.

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