27 Consider the vector a = -9ị- 3j. (a) Find â. (b) Find the vector b in the direction of a with a magnitude of 5.

Find the angle that the vector v = 5ij makes with the vector i (assume it is = measured in the counterclockwise direction). Put your answer in radians and round to two decimal places.

Find the angle a in radians between the vectors απ -3] and

The minute hand of a wall clock measures 24 cm from its tip to the axis about which it rotates. The magnitude and angle of the displacement vector of the tip are to be determined for three time intervals. What are the magnitude and angle from a quarter after the hour to half past, the magnitude and angle for the next half hour, and the magnitude and angle for the hour after that? (Use a coordinate system with the origin at the clock center, +x rightward toward the "3:00" position, and +y upward toward the "12:00" position.) (a) the magnitude from a quarter after the hour to half past cm(b) the angle from a quarter after the hour to half past ° (counterclockwise from the +x-axis)(c) the magnitude for the next half hour cm(d) the angle for the half hour in part (c) ° (counterclockwise from the +x-axis)(e) the magnitude for the hour after that cm(f) What is the angle for the hour in part (e) ° (counterclockwise from the +x-axis)