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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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Mathematical Method for Determining Resultants of Vectors that form right triangles! If two component vectors are at right angles to each other, their.

Mathematical Method for Determining Resultants of Vectors that form right triangles! If two component vectors are at right angles to each other, their.

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