Given two vectors Á = 4î + 3j and B = 12î – 5j a)Find the scalar product A · B. b)Find the angle between the two vectors. c)Find the vector product A × B.

Problem 20:  Assume you have two vectors, A = 7.1i + 3.9j and an unknown vector B with length 3.2. In this problem, you must assume that both components of B are positive, Bx > 0, and By > 0. Part (a)  If the scalar product of these two vectors is A⋅B = 16.3, what is the x-component of the vector B? You may assume that Bx > 0. Part (b)  What is the y-component of the vector B? Again, assume By > 0.

Find a unit vector perpendicular to A = (î+ ĵ – Îk) and B = ( 2i + j- 3k). (Hints. One method to find the unit vector C perpendicular to A and B will be to use the fact that the cross product is perpendicular to both vectors A and B, but keep in mind that the magnitude of the unit vector is one. There is another method which is a little bit longer by using the fact that the dot product AC=0 and BC=0 where C is the unit vector )

For the vectors shown in the figure, find the magnitude and direction of the vector product A C. B' 6. 70° 40° 8. 48, directed out of the page 45. directed out of the page O 16. directed out of the page O 48, directed into the page O 45, directed into the page ) 16, directed into the page

Problem 20:  Assume you have two vectors, A = 7.1i + 3.9j and an unknown vector B with length 3.2. In this problem, you must assume that both components of B are positive, Bx > 0, and By > 0. Part (a)  If the scalar product of these two vectors is A⋅B = 16.3, what is the x-component of the vector B? You may assume that Bx > 0. Part (b)  What is the y-component of the vector B? Again, assume By > 0.

Q2. Here is a plot of the velocity vs. time for an car. Take a look at the plot and answer each of the following questions: 1. Describe the car's velocity vs. time. For example..."At the beginning of the plot the car was traveling at a velocity of ____ After seconds of constant velocity the car..." 2. What is the initial velocity of the car and how many seconds does the car travel at this velocity? 1. What distance does the car travel while at the initial velocity? 3. What is the final velocity of the car? 4. During what section of the plot (start & stop times) does the car accelerate? 1. How many seconds does the car accelerate? 2. What is the velocity before the acceleration (vi)? 3. What is the velocity after the acceleration (vf)? 4. Calculate the car's average acceleration over this period. 5. During what section of the plot (start & stop times) does the car decelerate? 1. How many seconds does the care decelerate? 2. What is the velocity before the deceleration (vi)? 3. What is…