Consider the x - axis as representing east, the y - axis as north and z - axis as vertically upwards. Give the vector representing each of the following points and the direction is of 45°.
a) 5 m north east and 2 m up
b) 4 m south east and 3 m up
c) 2 m north west and 4 m up

Explanation

`X = 2 cos 45^(@) = (2)/(sqrt(2)) hat (i)`
`Y = 2 sin 45^(@) = (2)/(sqrt(2)) hat (j)`
`Z = 4m = 4 hat (k)`
`:. (- hat(i) + hat(j)) sqrt(2) + 4 hat(k)`