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Vector Addition and Subtraction Do Now Differentiate between a vector and scalar Give an example of each Parallel Vectors Add like numbers on a number line. 5 8 5 + 8 = 13 5 8 8-5=3 Perpendicular Vectors Use Pythagorean’s Theorem to determine the magnitude Use Tangent to determine the direction Example A person walks 40 m north and then 30 m east. What is their displacement? b a a2 + b2 = c2 302 + 402 = c2 c = 50m tan = opp/adj = tan–1 (b/a) Graphical Method Assign a scale to the vectors ex. 1N in problem = 1cm in diagram Draw vectors head to tail using a protractor to determine direction and a ruler to determine magnitude. Draw the resultant vector. Measure its magnitude with a ruler and its direction with a protractor Parallelogram Rule When two vectors have a tail at the same place, they may be added together by moving the tail of one to the head of the other using a parallelogram. b b ad = ab + bd d a a c c Sample Problem Solve Graphically and Algebraically A plane flies with a velocity of 52 m/s east through a 12 m/s cross wind blowing the plane south. Find the magnitude and direction (relative to due east) of the resultant velocity at which it travels. An ambitious hiker walks 25 km west and then 35 km south in a day. Find the magnitude and direction (relative to due west) of the hiker's resultant displacement. Adding Vectors that are not Perpendicular Select a coordinate system. Draw and label vectors Find the x and y components of all vectors using trigonometric functions SohCahToa Use Pythagorean Theorem to find the magnitude of the resultant vector. Use trigonometric function to find the angle of the resultant vector.