A ship sets out to sail to a point 124 km due north. An unexpected storm blows the ship to a point 72.6 Ian to the north and 31.4 km to the east of its starting point. How far, and in what direction, must it now sail to reach its original destination?

Consider two vectors given as:

Then the sum (say ) of the above two vectors can be stated in unit vector notation as:

The magnitude of vector is:

The angle ( ) made by the vector c with the horizontal is given as:

Given:

(a) From above it is clear that the sum of the vectors and vector can be given in the unit vector notation as:

Comparing the given vectors to the vectors represented by equation (1) and (2), we have

Therefore the sum of the vectors is given by equation (3) as:

Therefore the sum of the vectors in unit vector notation is .
(b)The magnitude of can be calculated using equation (4) as:




Substituting the values of component of vector and vector , we have

Therefore the magnitude of sum of vectors and is .
The direction of vector can be calculated using equation (5) as:

Substituting the values of component of vectors and , we have

Therefore the vector subtends an angle of 68.1° with the horizontal.