1.2 Vectors and scalars Understandings: Applications and skills: · Vector and scalar quantities · Combination and resolution of vectors · Vector and scalar quantities . Combination and resolution of vectors Scalars Examples: tip Vectors a tail Examples: Scalar Multiples of Vectors Multiplying a vector by a constant simply scales the magnitude (arrow length) up or down. If we multiply by a negative value, it scales the vector up or down AND reverses the direction of the vector. e.g. r 3r 1 1 - To - 2r Addition of Vectors: Vector quantities are added differently than scalars. We can use diagrams to model this. Vector addition: Add the vectors 'TIP to TAIL' a +b =b+ a
a b a + b = Notice that it doesn't matter which order you add the vectors in. You get the a +b b a same result! Subtraction of Vectors Vector subtraction is essentially addition, just with one of the vectors reversed before adding. e.g. Find a - b a - b b a - b a Examples: a) 6 m [E] + 18 m [W] b) 2.4 ms 1 [N] + 7.1 ms" ' [S] c) A car travels 36.0 km [N] and then 77.0 km [W]. Find the displacement of the car (magnitude and direction) using a scale diagram, and then using Pythagorean theorem and trigonometry.
Resolution of Vectors Every vector in 2-D can be resolved into its horizontal and vertical parts using basic trigonometry. e.g. v =50.0 ms"1 V, 29 F=71.0N Fy 36° v x x 55. Which of the following contains three scalar quantities? A. mass charge speed B. density weight mass C. speed weight charge D. charge weight density 56. Which one of the following quantities is a vector? A. Work B. Temperature C. Electric field D. Pressure 57. Which one of the following includes three vector quantities? (1) (1)