1. Show the following properties are true. Be sure to state your vectors before you show the property is true (example: = < a, b>) (8 points) = ( ) = k = k( ) = (k) = | | 2 2. If is the angle between two non zero vectors and , where 0 180 then: = || || Find the angle between the two vectors. (9 points) a. = < 7, -1> and = < 2, 2> b. = < 2, 10> and = < 5, -2> c. = < 2, -6> and = < 6, 2> 3. Fill in the right column of the chart with Positive, Negative, 0 or Cannot be determined. ( 9 points) Be sure to show at least 1 new example to prove your choice for each case (a vector pair not used in the earlier part). Always show and explain your work for each example. If the angle between the vectors and is: Then the dot product will be: Obtuse ________________________ Right ________________________ Acute ________________________ 4. Do a little research. Where is dot product used in "the real world