PREVNEXTSUBMITMenuResourcesGlossaryNotesClear and return to MenuSearch ResultsFilterSlide TextNotesSearch in:Check to includeSearch...TermsDefinitiondefinitionresourcessearchpauseplayreplaysubmitnextpreviousvolumeadding vectors: pythagorean method during a car ride into the desert, leah travels 20 km [n], turns left and travels 50 km [w] and then turns left again and travels 30 km [s]. what is lisa's total displacement? during a car ride, leah travels 20 km [n], turns left and travels 50 km [w] and then turns left again and travels 30 km [s]. what is lisa's total displacement? first, sketch out the problem using vector diagrams: 20 km [n] 50 km [w] 30 km [s] 1. add parallel vectors until you are left with two vectors at right angles to one another lets choose north as positive 20 km [n] = +20 30 km [s] = -30 net vector = +20 + (-30) = - 10 -10 = 10 km [s] + = therefore the resultant north-south vector is 10 km [s], our other vector is 50 km [w] and these two vectors will form a right angle with one another. 2. draw the 2 perpendicular vectors tip to tail and draw in the resultant vector. 50 km [w] 10 km [s] resultant vector 3. apply the pythagorean theory(a2 + b2 = c2) to determine the length of the resultant vector. b = 50 a = 10 c = ? therefore the magnitude of the displacement is 51 km. next, we need to determine the direction. 4. determine the direction of the resultant vector by finding the angle between the resultant vector and the vertical vector. this can be done using trigonometric ratios. 50 km [w] 10 km [s] 51 km [?] θ therefore the direction of displacement is [s 79˚w] 5. combine your magnitude and direction to write out the net vector. therefore, lisa's total displacement is 51 km [s 79˚ w] 50 km [w] 10 km [s] 51 km [s 79˚ w] 79º˚