# Components of unit vectors

• roam
In summary, a golfer takes three putts to get the ball into the hole of a level putting green. The first putt displaces the ball 2.5 m North, the second 4.8 m South-East, and the third 5.7 m South-West. The displacements can be expressed in unit vector notation as (0)i, (2.5)j, (3.39)i, (-3.39)j, and (-4.03)i, (-4.03)j. To determine the angle in degrees for a single putt, the resultant of these three vectors must be found and then the angle can be calculated using the formula tanθ = y/x.

## Homework Statement

A golfer takes three putts to get the ball into the hole of a level putting green. The first putt displaces the ball 2.5 m North, the second 4.8 m South-East and the third 5.7 m South-West.

Express each of these three displacements in unit vector notation where i is a unit vector pointing due East and j is a unit vector pointing due North.

E.g the first displacement is: $$(0)i, (2.5)j$$

## The Attempt at a Solution

The first one is obvious but the other two aren't. For example for the second part the question says it is 4.8 m South-East BUT it doesn't say how many degrees due South-East. Without the angle, it is impossible for me to find the rectangular components (i.e $$4.8 sin(\theta), 4.8 cos(\theta)$$). Any suggestions?

When they say south of east or south of west the angle is always 45 degrees with east-west line.

Oh thanks! I found the three displacements in unit vector notation:

$$0i, 2.5j$$
$$3.39i, -3.39j$$
$$-4.03i, -4.03j$$