Given the following vector, v, obtain the unit vector (u) that aligns with the direction of  v.

v = 11 i - 7 j

Draw the following vector and consider the origin as its initial point. Then, calculate its magnitude.

v = 12i + 3j

Find ||a + b||² - ||a - b||² using the following vectors:

a = -5i + 6j, b = 2i + 7j

A vector is shown in the figure. Write it in the form 〈a, b〉. Express your answers as exact values or round them to four decimal places, if necessary.

Two forces of 180 and 350 newtons act on a point in the passenger train. Calculate the magnitude of the resultant force if the angle between them is $78°$.

A garbage truck is parked on a hilly road. If the weight of the truck is 7200 lb and the angle between the road and the horizontal is 21°, what is the force required to keep the truck on its position?

A luxury ship starts from point P and covers a distance of 12.9 km with a bearing of $209°$. After reaching point Q, the ship turns back and covers a distance of 5.8 km with a bearing of $347°$ . Calculate the distance of the ship from the starting point.