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

`Y = y cos 45^(@) = (4) /(sqrt(2)) hat (i)`
` X = y sin 45^(@) = - (4)/(sqrt(2)) hat(j)`
`Z = 3 m = 3 hat (k)`
`:. (40)/(sqrt(2)) (hat(i) - hat(j)) + 3 hat (k)`