Compute the x- and y-components of the vectors$\overrightarrow{A},\overrightarrow{B},\overrightarrow{C}\mathbf{and}\overrightarrow{D}$in Fig. E1.24.

Here, vector is easily defined with the help of its magnitude and its angle with the x and the y axis.

Here in this case, there are four given vectors.

For this vector we will use the given magnitude as well as the angle with the x axis and the y axis.

For the direction shown in the graph,

$\overrightarrow{A}$=(0,-8) in meters

Here, the vector is exactly on the y axis so, the magnitude with respect to y axis will be zero.

For vector B, the angle of the vector made with the x axis will be 90 – 30,

that is the angle made will be 60.

Hence,the components of the B vector will be magnitude multiplied by the cos angle and sin angle made with respect to x axis.

$\overrightarrow{B}=15\cos 60+15\sin 60$

By putting the value of cos 60 = ½ and sin 60 =$\sqrt{3}$/2

We get,

$\overrightarrow{B}$=(7.5 , 13) in meters

Similarly for vector C

$\overrightarrow{C}=-12\cos 25-12\sin 25$

After the putting the value of cos 25 and sin 25,

C = (-10.88,-5.07) in meters

The coordinates for vector D will be,

$\overrightarrow{D}=-10\cos 53+10\sin 53$

D = (-7.99, 6.02) in meter

Hence, the coordinates of A, B, C and D are (0,-8) ; (7.5 , 13); (-10.88,-5.07) and (-7.99, 6.02), respectively.