Skip the following Questions:

• "Sailing Analogy" - Questions 1.8 & 1.9
• "Dot Products in Mechanics" - Question 1.10 (1, 2, 3)

PLEASE HELP ANSWER THE FOLLOWING (COMPREHENSIVELY) AND SKIP THE QUESTIONS MENTIONED ABOVE. DOING THEM WILL HELP ME THOUGH

1 Dot Product Basics 1.1 Denition and Calculations The dot product allows us take two vectors and produce a scalar quantity. It can be calculated two different (but equivalent ways): Either using the magnitudes of the vectors and the angle between them: rig: |1HE|cos6AB (1) E 9i A Or by multiplying their roomponents together, multiplying their y-components together, and summing up the result: A'B =AIBE+Ava It's easy to extend this method to higher dimensional vectors: Question 1.1) In three dimensions, how would you calculate the dot product of two vectors A and B if you know their my, z-components? Question 1.2) What is the dot product of two perpendicular vectors equal to? Question 1.3) Under what circumstances will the sign of a dot product of vectors be negative? {NJ '8 B c D Question 1.4) Consider the vectors If, RC", 5 diagrammed above. Graph each of the listed pairs of vectors, write down their components in i, j notation and calculate their dot product. Use your result to determine the angle between the vectors. 1' IT and 15+ E (example) 4, 200, and 2l+1 ' (AM?) 2 L 1I+I| _\\/>