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 .5 m north east and 2 m up,

Consider the x-axis as representing east, the y-axis as north and z-ax

1.	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 .5 m north east and 2 m up,
Answer» 5 m north east and 2 m up 4 m south east and 3 m up 2 m north WEST and 4 m up Solution :(a) LENGTH ALONG X-axis `=5cos45^(@)=(5)/(sqrt2)m` Length along Y-axis `=5sin45^(@)=(5)/(sqrt2)m` Length along Z-Axis =2m `:.` In vector rotation `=(5)/(sqrt2)hati+(5)/(sqrt2)hatj+2hatk=(5(hati+hatj))/(sqrt2)+2hatk` (b) Length along `X =4cos45^(@)=(4)/(sqrt2)m` Length along `Y=4sin45^(@)=(4)/(sqrt2)m` Length along Z-axis =3m In vector rotation `=(4)/(sqrt2)hati-(4)/(sqrt2)hatj+3hatk=4(hati-hatj)//sqrt2+3hatk` (c) Length along `X=-2cos45^(@)=-(-2)/(sqrt2)m=-sqrt2m` Length along `Y=2sin45^(@)=(2)/(sqrt2)m=sqrt2m` length along Z=4m `:.` In vector rotation `=-sqrt2hati+sqrt2hatj+4hatk=(-i+j)sqrt2+4hatk`.