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Adding Vectors that are not perpendicular Holt Physics Chapter 3 Section 2 (continued) 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 Vector 1 No right triangle! Non-perpendicular vectors This will require new “old” variables For Displacement Vectors Vector #1 Δx1 Δy1 DR1 θ1 Vector #2 Δx2 Δy2 DR2 θ2 Resultant ΔxT ΔyT DRT θR Non-perpendicular vectors Step #1 You must resolve vector #1 into x & y components Vector 1 DR1 Δy1 θ1 Δx1 Non-perpendicular vectors Step #2 You must resolve vector #2 into x & y components DR2 Δy2 Vector 2 Δx2 θ2 Non-perpendicular vectors Step #3 Add all X components to find ΔxT Δx1 + Δx2 = ΔxT Δx1 Δx2 ΔxT Non-perpendicular vectors Step #4 Add all Y components to find ΔyT Δy1 + Δy2 = ΔyT Δy2 ΔyT Δy1 Non-perpendicular vectors Step #5 Now you have total x & y components Use Pythagorean theorem to find resultant DRT2 = ΔxT2 + ΔyT2 DRT ΔyT θR ΔxT Non-perpendicular vectors Step #6 Use tangent to find the angle - Same equations - Tan θR = ΔyT ΔxT θR = Tan-1 (ΔyT / ΔxT) 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 θR ΔyT ΔxT 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.